system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall. Use the code interpreter (Python; sympy/numpy/scipy available) to recompute rather than trusting arithmetic.

Solve the given problem. Show your reasoning.

Use web search for anything you're even remotely unsure about.

user

For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/

reasoning

{
 "summary": [
  "**Verifying interlab agreements**\n\nI need to focus on providing the answer specifically as asked. This seems like a question regarding whether any interlab agreements exist. I need to verify that information, which means I should inspect relevant papers and conduct a search on the web for more details. It's important to ensure that I'm getting accurate, relevant information to fully address the user's question without adding any extra details."
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "OpenFlexure microscope three independent labs resolution field curvature illumination uniformity stage repeatability certified targets uncertainties",
   "site:royalsocietypublishing.org/rsta OpenFlexure microscope field curvature illumination uniformity repeatability",
   "\"OpenFlexure\" \"field curvature\" illumination uniformity",
   "\"OpenFlexure microscope\" \"three\" labs repeatability"
  ],
  "query": "OpenFlexure microscope three independent labs resolution field curvature illumination uniformity stage repeatability certified targets uncertainties"
 }
}

reasoning

{
 "summary": [
  "**Searching for study details**\n\nIt seems like there isn't a three-lab study to reference. I need to be cautious and check what the papers actually report. I'll open up full PMC resources and Collins, then search for terms related to this topic. It's important to find the right information, so I’ll ensure I'm thorough in my search while reviewing the papers carefully to verify their content!"
 ]
}

web_search

{
 "action": {
  "pattern": "resolution",
  "type": "find_in_page",
  "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC11448745/"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://eprints.gla.ac.uk/327438/2/327438.pdf"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://eprints.gla.ac.uk/327438/2/327438.pdf"
 }
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "10.1364/BOE.385729 pdf OpenFlexure",
   "Collins 2020 OpenFlexure microscope PDF resolution repeatability"
  ],
  "query": "10.1364/BOE.385729 pdf OpenFlexure"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://scispace.com/pdf/robotic-microscopy-for-everyone-the-openflexure-microscope-29lezyitps.pdf"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC7249832/bin/boe-11-5-2447.pdf"
 }
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "https://pmc.ncbi.nlm.nih.gov/articles/PMC7249832/bin/boe-11-5-2447.pdf"
  ],
  "query": "https://pmc.ncbi.nlm.nih.gov/articles/PMC7249832/bin/boe-11-5-2447.pdf"
 }
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "site:pmc.ncbi.nlm.nih.gov/articles/PMC7249832 \"repeatability\"",
   "site:pmc.ncbi.nlm.nih.gov/articles/PMC7249832 \"USAF\"",
   "site:pmc.ncbi.nlm.nih.gov/articles/PMC7249832 \"field curvature\"",
   "site:pmc.ncbi.nlm.nih.gov/articles/PMC7249832 \"illumination\""
  ],
  "query": "site:pmc.ncbi.nlm.nih.gov/articles/PMC7249832 \"repeatability\""
 }
}

reasoning

{
 "summary": [
  "**Evaluating research methods**\n\nI'm considering whether I could use the NCBI API with efetch for a direct URL search, but it seems that might not be necessary. The core question I'm facing is likely binary. I definitely need to verify the literature up to the current 2026 to see if new studies exist. It feels like I need to search for broader exact metrics to get a full picture of the topic at hand."
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "OpenFlexure microscope interlaboratory comparison optical performance resolution uniformity stage repeatability",
   "OpenFlexure microscope reproducibility study labs certified target MICAT",
   "OpenFlexure microscope metrology multi-site validation",
   "OpenFlexure microscope illumination uniformity resolution field curvature stage repeatability study"
  ],
  "query": "OpenFlexure microscope interlaboratory comparison optical performance resolution uniformity stage repeatability"
 }
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "\"Robotic microscopy for everyone\" \"480 nm\"",
   "\"Robotic microscopy for everyone\" \"1–4\" µm repeatability",
   "\"OpenFlexure microscope\" \"stage repeatability\"",
   "\"OpenFlexure microscope\" \"illumination uniformity\""
  ],
  "query": "\"Robotic microscopy for everyone\" \"480 nm\""
 }
}

output

**No.** As of August 31, 2026, the published evidence does not establish agreement across three independent laboratories within stated measurement uncertainties.

Reasoning:

- Collins *et al.* report approximately **480 nm central-field resolution** from an edge on a USAF 1951 target. Field curvature is only described qualitatively as reducing edge resolution; illumination non-uniformity/vignetting is discussed and corrected computationally. This is not a three-laboratory comparison and provides no interlaboratory uncertainty budget. ([pmc.ncbi.nlm.nih.gov](https://pmc.ncbi.nlm.nih.gov/articles/7249832/?utm_source=openai))
- Knapper *et al.* describe MICAT calibration using a USAF target, camera/illumination calibration, and image-feedback stage calibration as a proposed self-certification and quality-control framework. They present no comparative measurements from three laboratories and explicitly report no additional dataset. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
- Distributed manufacture in multiple countries demonstrates buildability, not metrological reproducibility. No located study jointly quantifies resolution, field curvature, illumination uniformity, and stage repeatability against certified, traceable targets with stated uncertainties at three independent sites. ([pmc.ncbi.nlm.nih.gov](https://pmc.ncbi.nlm.nih.gov/articles/7249832/?utm_source=openai))

Therefore, the correct conclusion is **“not demonstrated,” rather than “yes” or evidence of disagreement**. A coordinated three-site interlaboratory study with matched protocols, traceable targets, replicate instruments, and uncertainty budgets remains necessary.

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You formalize solutions into proofs. The solutions you receive were
generated by an LLM and may contain hallucinations, wrong facts, or
flawed reasoning: treat every claim as potentially wrong, and do not
assume the solver's reasoning is valid unless you can justify it.

On every call, you must choose one of two actions:

- action="proof": Produce a formal proof for the solution (see
  proof format below). This is the default — start by trying to
  formalize.
- action="reject": If while formalizing you find any substantive
  issues with the solution (incorrect facts, flawed reasoning,
  missing cases, etc.), reject the solution and set reject_reason
  to explain what's wrong; the solver will get this and retry.

A proof is a sequence of states. Each state is a list of strings.
Index 0 is the expression being solved for. It starts as a goal
variable (like "ANSWER") and ends when resolved.

Each step has: state (full list of strings after this step),
justification_type ("citation", "problem_given", or "computation"),
and justification (why).

One transformation per step. Every step must be justified.

When a step's justification is a named mode of inference, use
justification_type: citation. The cited "result" is the mode of
inference itself.

PREMISES MUST BE EXPLICIT. When a step relies on a premise that
isn't already in the previous state — including bounds, conditions,
edge cases, factual claims, or assumptions like "X is a Y" — you
MUST first add a step that introduces the premise explicitly. That
added step needs its own justification. Do not bury premises in
justification text. If you cannot justify a premise, your proof
must handle the case without it (e.g., by considering all cases).

Use web search for anything you're even remotely unsure about.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Solution: **No.** As of August 31, 2026, the published evidence does not establish agreement across three independent laboratories within stated measurement uncertainties.

Reasoning:

- Collins *et al.* report approximately **480 nm central-field resolution** from an edge on a USAF 1951 target. Field curvature is only described qualitatively as reducing edge resolution; illumination non-uniformity/vignetting is discussed and corrected computationally. This is not a three-laboratory comparison and provides no interlaboratory uncertainty budget. ([pmc.ncbi.nlm.nih.gov](https://pmc.ncbi.nlm.nih.gov/articles/7249832/?utm_source=openai))
- Knapper *et al.* describe MICAT calibration using a USAF target, camera/illumination calibration, and image-feedback stage calibration as a proposed self-certification and quality-control framework. They present no comparative measurements from three laboratories and explicitly report no additional dataset. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
- Distributed manufacture in multiple countries demonstrates buildability, not metrological reproducibility. No located study jointly quantifies resolution, field curvature, illumination uniformity, and stage repeatability against certified, traceable targets with stated uncertainties at three independent sites. ([pmc.ncbi.nlm.nih.gov](https://pmc.ncbi.nlm.nih.gov/articles/7249832/?utm_source=openai))

Therefore, the correct conclusion is **“not demonstrated,” rather than “yes” or evidence of disagreement**. A coordinated three-site interlaboratory study with matched protocols, traceable targets, replicate instruments, and uncertainty budgets remains necessary.

Formalize this into a proof, or reject if it has errors.

reasoning

{
 "summary": [
  "**Verifying sources for user solution**\n\nI need to verify the sources for the conclusion about the user’s solution dated August 31, 2026. It looks like I need to search for exact papers that provide formal proof. The current date is indeed August 31, 2026, according to the developer instructions. Therefore, I’ll look into web sources, focusing specifically on primary technical papers to find the best support for the conclusion. Let’s get started on that search!"
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "site:pmc.ncbi.nlm.nih.gov/articles/PMC7249832 OpenFlexure microscope resolution 480 nm field curvature illumination",
   "Knapper Developing the OpenFlexure Microscope towards medical use 2024 PDF MICAT calibration USAF target no additional data",
   "site:royalsocietypublishing.org/doi/10.1098/rsta.2023.0257 OpenFlexure MICAT calibration dataset",
   "OpenFlexure three laboratories resolution field curvature illumination uniformity stage repeatability certified targets"
  ],
  "query": "site:pmc.ncbi.nlm.nih.gov/articles/PMC7249832 OpenFlexure microscope resolution 480 nm field curvature illumination"
 }
}

reasoning

{
 "summary": [
  "**Investigating resolution claims**\n\nI see a potential issue regarding the \"approximately 480 nm central resolution.\" It seems the source text is missing some numbers due to math errors, but I'm thinking it's likely referring to 480 nm. I need to inspect this more closely. Also, Knapper might reference a newer 2023 paper discussing data and quantitative calibration, but it seems crucial to clarify evidence regarding lab comparisons. The absence of claims makes it hard to support our arguments, so I should search for literature evidence up to 2026."
 ]
}

web_search

{
 "action": {
  "pattern": "480 nm",
  "type": "find_in_page",
  "url": "https://pmc.ncbi.nlm.nih.gov/articles/7249832/"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://opg.optica.org/boe/viewmedia.cfm?seq=0&uri=boe-11-5-2447"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://eprints.gla.ac.uk/327438/"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://eprints.gla.ac.uk/327438/2/327438.pdf"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content"
 }
}

reasoning

{
 "summary": [
  "**Searching for agreement across labs**\n\nI'm trying to determine if all four agree across three labs, accounting for uncertainties. If I answer \"no,\" I'll need to show evidence that no study exists to support this. Therefore, I’ll search for the latest studies up to 2026, using Scholar and looking for exact terms. It's crucial I gather accurate and relevant information to clarify if there’s any consensus or disagreement among the studies."
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "\"OpenFlexure Microscope\" \"field curvature\" repeatability illumination uniformity",
   "\"OpenFlexure\" interlaboratory OR \"three laboratories\" OR \"three labs\" microscope",
   "\"OpenFlexure Microscope\" metrology uncertainty resolution stage repeatability",
   "\"OpenFlexure\" \"illumination uniformity\" resolution target"
  ],
  "query": "\"OpenFlexure Microscope\" \"field curvature\" repeatability illumination uniformity"
 }
}

reasoning

{
 "summary": [
  "**Evaluating evidence search**\n\nI’m considering formalizing the approach by using an evidence set that indicates principal papers are lacking. I need to ensure that proof validity relies on the premise that \"no published evidence reports\" can justify my findings, which means I’ll have to conduct a thorough literature search. It may not be ideal to cite the search results directly, but I could reference OpenFlexure publications to illustrate the corpus and inspect the search page publications."
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "site:openflexure.org publications OpenFlexure microscope papers calibration resolution",
   "site:openflexure.gitlab.io publications OpenFlexure microscope",
   "site:pubmed.ncbi.nlm.nih.gov OpenFlexure microscope",
   "site:crossref.org OpenFlexure microscope"
  ],
  "query": "site:openflexure.org publications OpenFlexure microscope papers calibration resolution"
 }
}

reasoning

{
 "summary": [
  "**Evaluating citation syntax**\n\nI see that the full list can get a bit unwieldy, but that's okay. I should clarify step justifications. At my final state, I can index 0 as \"ANSWER = No—...\" and keep the remaining premises. They might be fine. The process ends when the issue is resolved. Also, I wonder if the citations in JSON strings should render correctly. I need to confirm what the exact syntax for the citations is."
 ]
}

output

{
 "action": "proof",
 "proof": {
  "initial_state": [
   "ANSWER"
  ],
  "steps": [
   {
    "state": [
     "ANSWER",
     "A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment."
    ],
    "justification_type": "problem_given",
    "justification": "This is the conjunctive evidentiary requirement stated in the question."
   },
   {
    "state": [
     "ANSWER",
     "A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.",
     "Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories."
    ],
    "justification_type": "citation",
    "justification": "Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))"
   },
   {
    "state": [
     "ANSWER",
     "A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.",
     "Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.",
     "Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition."
    ],
    "justification_type": "computation",
    "justification": "The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study."
   },
   {
    "state": [
     "ANSWER",
     "A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.",
     "Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.",
     "Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.",
     "Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data."
    ],
    "justification_type": "citation",
    "justification": "The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))"
   },
   {
    "state": [
     "ANSWER",
     "A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.",
     "Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.",
     "Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.",
     "Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.",
     "Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established."
    ],
    "justification_type": "computation",
    "justification": "A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement."
   },
   {
    "state": [
     "ANSWER",
     "A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.",
     "Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.",
     "Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.",
     "Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.",
     "Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.",
     "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."
    ],
    "justification_type": "citation",
    "justification": "Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))"
   },
   {
    "state": [
     "ANSWER",
     "A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.",
     "Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.",
     "Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.",
     "Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.",
     "Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.",
     "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.",
     "Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement."
    ],
    "justification_type": "computation",
    "justification": "Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study."
   },
   {
    "state": [
     "ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.",
     "A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.",
     "Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.",
     "Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.",
     "Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.",
     "Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.",
     "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.",
     "Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement."
    ],
    "justification_type": "computation",
    "justification": "Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement."
   }
  ]
 },
 "reject_reason": ""
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You audit state 0 (the initial state) of a proof. State 0 never
gets a justification, so anything here flows through the proof
unchecked. The formalizer may choose its own representation, but
the content must come from the problem, not be made up.

Initial state: ['ANSWER']
Problem text:  For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Two checks:

1. state[0] must be a goal — "ANSWER", "ANSWER = ?", or a
   restatement of what the problem asks for in abstract or
   symbolic terms. Not a definition, not a premise, not a
   specific conclusion.

2. Every other entry's content must be IN the problem text.
   Notational translation is fine — restating things in symbols,
   switching between equivalent formulations, defining a
   shorthand for an object the problem names. What's NOT fine
   is content the formalizer ADDED: a derived fact, a computed
   value, an assumed constraint, a theorem the problem doesn't
   invoke, a definition the problem doesn't give, etc. If the
   formalizer had to reason or compute to produce the entry,
   it belongs in a justified step, not here.

REJECT if state[0] isn't a goal, OR if any entry contains
content that isn't derivable from a careful reading of the
problem text alone (no reasoning steps required).

ACCEPT otherwise.

When rejecting, exhaustively list every issue you find with the
step as a separately numbered point. Don't stop at the first error
or issue — enumerate all of them.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Initial state (state 0): ['ANSWER']

Full proof for context:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

output

{
 "accepted": true,
 "reason": "State 0 contains only “ANSWER,” which is an allowed goal placeholder, and it contains no added premises, conclusions, computations, or other unsupported content."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You are auditing step 1 of a proof generated by an LLM.
LLMs hallucinate, including misquoting or fabricating things they
claim are in the problem text. Your job is specifically to FIND
ERRORS. Treat every claim with skepticism.

The step claims this value is directly stated in the problem text:
  BEFORE: ['ANSWER']
  AFTER:  ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  CLAIM:  This is the conjunctive evidentiary requirement stated in the question.

The problem text is:
  For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Check whether the step relies on any premise (assumption, bound,
edge case, or factual claim) that is not already present in the
previous state or the problem text. If you can identify such an
unstated premise, reject the step — the proof must make all
premises explicit before using them.

Accept ONLY if the problem text explicitly states this value, or
something clearly isomorphic/equivalent; if the only difference is
basic notation, accept. Reject if the value is inferred, assumed,
not actually in the text, or relies on a hidden premise.

When rejecting, exhaustively list every issue you find with the
step as a separately numbered point. Don't stop at the first error
or issue — enumerate all of them.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 1 being judged:
  Previous state: ['ANSWER']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  Justification type: problem_given
  Justification: This is the conjunctive evidentiary requirement stated in the question.

output

{
 "accepted": false,
 "reason": "1. The problem does not state that the measurements must be published; “published” is an added evidentiary premise.\n2. The problem says “across three independent labs,” not “at least three independent laboratories.” Treating this as a minimum of three is an interpretation rather than a directly stated value."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You extract the exact source text a proof step rests on, so an engine can
verify the extraction mechanically. The engine aligns every quote you return
against the source token-by-token and records the aligned source span. A
separate analyst then judges whether the engine-verified spans actually
license the step.

# Goal
By justification type:

- `problem_given` — the step claims the problem statement says so. Set
  `source_kind: "problem"`, copy the problem statement into `source_text`
  EXACTLY as given (the engine rejects any deviation), `source_url: ""`, and
  put in `quotes` the substring(s) of the problem statement the step relies on.
- `citation` — the step invokes a named theorem, law, identity, or definition.
  Find the canonical published statement; one authoritative fetchable source
  is enough — stop searching once you have it. Set `source_kind: "fetched"`
  and `source_url` to where you read it — **the engine fetches that URL itself
  and aligns your quotes against the page text it receives**, so the URL must
  be publicly fetchable static HTML or plain text: no paywalls, no login, no
  JavaScript-rendered content (prefer reference pages like Wikipedia,
  MathWorld, ProofWiki, or published lecture notes). `source_text` is your
  record of the relevant passage; the engine audits it but aligns against its
  own fetch.

`claim_mapping`: one or two sentences on how the quotes license this step's
BEFORE -> AFTER transformation — including what they do NOT cover, if the
justification claims more than the source states.

# Success criteria
- Quotes are copied from the source, not composed. Alignment tolerates
  whitespace, line-wrap, casing, and typographic punctuation; a paraphrased
  or reworded quote is discarded as "no grounding".
- Quotes are the minimal spans that state the relied-on fact — not whole
  paragraphs, not fragments too short to assert anything. Avoid quoting across
  tables, formulas rendered as markup, or other HTML-heavy regions; prefer
  plain-prose statements of the result.
- For citations: a real, findable source; if a multi-part definition or
  theorem is involved, quote enough that cherry-picking would be visible.

# If there is nothing to extract
If the problem statement does not contain what the step attributes to it, or
no fetchable source states the cited result, return your best honest
extraction anyway (e.g. the nearest passage) and say in `claim_mapping` that
it does not support the claim — the analyst, not you, decides whether that is
a contradiction.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 1 to ground:
  Previous state: ['ANSWER']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  Justification type: problem_given
  Justification: This is the conjunctive evidentiary requirement stated in the question.

output

{
 "source_kind": "problem",
 "source_url": "",
 "source_text": "For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?",
 "quotes": [
  "resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties"
 ],
 "claim_mapping": "The quote makes agreement a conjunctive requirement covering all four named quantities, certified targets, three independent laboratories, and stated uncertainties. It does not explicitly require the measurements to be published, so that part of the new state is not grounded in the problem statement."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You are auditing step 2 of a proof generated by an LLM.
LLMs hallucinate facts, citations, definitions, and reasoning. Your
job is specifically to FIND ERRORS, not to confirm what looks
plausible. Treat every claim with skepticism.

The step claims this transformation is justified by a theorem, law,
identity, or definition:
  BEFORE: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  AFTER:  ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']
  CITED:  Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))

Decide: does the cited result exist, is it applied correctly here,
and does it justify every change from BEFORE to AFTER?

Verify by web search rather than plausibility or recall, in
particular:
- Introduced definitions ("X is defined as ..."): confirm the
  definition matches the canonical published source — the LLM may
  present one component of a multi-part definition as the whole
  thing.
- Steps that seem too basic to cite: even a move like "let x = ..."
  has a real underlying justification (definitional extension, a
  foundational rule of logic). Confirm the implicit foundational
  rule is real and correctly applied; do not reject a step just
  because its justification feels trivial.
- Specific factual claims you cannot derive by general reasoning:
  if you cannot verify such a claim after searching, reject the
  step.

Check whether the step relies on any premise (assumption, bound,
edge case, or factual claim) that is not already present in the
previous state or the problem text. If you can identify such an
unstated premise, reject the step — the proof must make all
premises explicit before using them.

Accept if the citation (or underlying justification) is real and
correctly applied, AND the step introduces no hidden premises.
Reject if the cited result doesn't exist, doesn't apply, doesn't
account for all changes in the state, smuggles in an unjustified
claim, or relies on a hidden premise.

When rejecting, exhaustively list every issue you find with the
step as a separately numbered point. Don't stop at the first error
or issue — enumerate all of them.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 2 being judged:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']
  Justification type: citation
  Justification: Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))

reasoning

{
 "summary": [
  "**Auditing claims and sources**\n\nI need to ensure I'm auditing the exact claims properly. This involves using the web and returning the exact JSON format that includes accepted boolean and reason strings. I also need to inspect the primary source of the paper, so I should search for the DOI or PDF to access it directly. This attention to detail is crucial for accuracy in my findings!"
 ]
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content"
 }
}

reasoning

{
 "summary": [
  "**Assessing Potential Errors**\n\nI need to assess some subtle errors. First, “using an edge on a USAF target” seems accurate. Regarding the “480 nm PSF FWHM over central 50%,\" I wonder if it correctly reports the FWHM of 480 nm for the entire central 50%. This could confuse one measured edge response with the region. I should confirm the reported corrections for sensor vignetting, check field curvature and aberration, and look into the absence of measurements from three independent laboratories. I need to verify everything!",
  "**Evaluating Technical Accuracy**\n\nI need to pay attention to the line spread function mentioned—it’s actually not a 2D PSF, but the paper refers to it as PSF. I should check whether the paper accurately reports cited results. The use of an edge on a USAF target seems valid, and yes, it uses the USAF resolution test target. However, I’m wondering about certification and if there are measurements from three independent labs mentioned. The citation isn't robust enough for broad claims. I should scrutinize the illumination uniformity and vignetting correction further, too."
 ]
}

web_search

{
 "action": {
  "pattern": "uncertaint",
  "type": "find_in_page",
  "url": "https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content"
 }
}

reasoning

{
 "summary": [
  "**Analyzing claims and measurements**\n\nI'm trying to make sure I have the details right for this output, focusing on the JSON format without any markdown. I'm reviewing some citations and wondering about the claims regarding measurements from multiple labs. The paper states a 480 nm point-spread-function FWHM but only examines it from one edge, which raises a question about whether it's truly applicable across the entire area mentioned. I'm thinking through whether this wording is misleading enough to prompt rejection of the claims. It’s important to be precise, so I'm paying close attention to every change.",
  "**Reviewing measurement details**\n\nThe paper notes a point spread function with a FWHM of 480 nm, which indicates it's nearly diffraction-limited, particularly over the central area. I see that \"this\" could refer to the performance, so that seems reasonable. When discussing the \"USAF target\" and related factors, I recognize issues like field curvature affecting resolution. It seems there aren’t uncertainties or multi-lab measurements, but I wonder if author affiliations count as independent labs. For citations, I think I need to include them, ensuring the output is valid JSON with Unicode for the reason string."
 ]
}

output

{
 "accepted": true,
 "reason": "The cited paper supports every added claim: section 2.2 derives a 480 nm PSF FWHM from an edge on a USAF resolution target, describes near-diffraction-limited performance over the central 50% of the field and decreased edge resolution caused by field curvature and aberration, and describes vignetting correction by overriding the lens-shading table. The paper contains no three-independent-laboratory comparison or associated uncertainty budgets. No hidden premise is introduced. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))"
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You name the one best source where a cited mathematical result can be read.
You do NOT quote from it — the engine will fetch the page itself, and a
separate agent will extract quotes from exactly what the engine receives.
Your only job is a good URL.

# Goal
The step invokes a named theorem, law, identity, or definition. Return:
- `url` — where the canonical statement can be read. The engine's fetcher is
  plain HTTP: the page must be publicly fetchable static HTML or plain text —
  no paywalls, no login, no JavaScript-rendered content. Prefer reference
  pages (Wikipedia, ProofWiki article pages, published lecture notes). One
  authoritative fetchable source is enough.
- `note` — one sentence: what you expect the page to state that licenses
  this step.

# If no fetchable source exists
Return `url: ""` with the note explaining what you looked for. An unnamed
source is a harmless no-op — never invent a URL that might not exist.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 2 to ground:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']
  Justification type: citation
  Justification: Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))

reasoning

{
 "summary": [
  "**Verifying source fetchability**\n\nI need to return a JSON object with the exact URL note. First, I should verify that the source is fetchable. If the given URL points to a static PDF or content, that won't work since I need it in HTML or plain text, PDFs are excluded. I could consider using a static HTML article from PMC. Okay, I’ll search for an appropriate source that fits these criteria. Let's get this sorted!"
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "Collins Robotic microscopy for everyone OpenFlexure microscope 480 nm point spread function FWHM USAF target section 2.2 PMC"
  ],
  "query": "Collins Robotic microscopy for everyone OpenFlexure microscope 480 nm point spread function FWHM USAF target section 2.2 PMC"
 }
}

reasoning

{
 "summary": [
  "**Checking lens shading table**\n\nI need to ensure that the vignetting lens shading table is present in the PMC. I’m thinking it might be important for whatever project I'm working on. Maybe I should take a closer look at any relevant materials or resources that could help. It feels crucial to get this right, so I want to double-check to avoid missing any important details about the shading table! I'll open the relevant documents and examine them."
 ]
}

web_search

{
 "action": {
  "pattern": "lens shading",
  "type": "find_in_page",
  "url": "https://pmc.ncbi.nlm.nih.gov/articles/7249832/"
 }
}

reasoning

{
 "summary": [
  "**Searching public content**\n\nI’m considering that PMC is generally public and static. However, I wonder if the recaptcha engine might fetch plain HTTP content too. I’ve seen search results that show the content. It could be useful to look into EuropePMC’s full-text HTML or the NCBI classic. I think I’ll proceed with an exact search to gather the right information. It’s all about finding what works best!"
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "Europe PMC PMC7249832 full text OpenFlexure 480 nm lens shading table",
   "site:opg.optica.org/boe/fulltext.cfm 385729 OpenFlexure microscope"
  ],
  "query": "Europe PMC PMC7249832 full text OpenFlexure 480 nm lens shading table"
 }
}

output

{
 "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC7249832/",
 "note": "Section 2.2 reports a 480 nm PSF FWHM over the central 50% of the field using a USAF target, edge degradation from field curvature and aberration, and lens-shading correction for vignetting, but presents no three-laboratory uncertainty comparison."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the code interpreter (Python; sympy/numpy/scipy available) to recompute rather than trusting arithmetic.

You are auditing step 3 of a proof generated by an LLM.
LLMs hallucinate and make subtle math errors that look correct on
a casual read. Your job is specifically to FIND ERRORS. Recompute
everything from scratch — do not trust the LLM's arithmetic or
algebra.

The step claims this is a correct computation:
  BEFORE: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']
  AFTER:  ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']
  CLAIM:  The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.

Verify the math by recomputing it yourself.

Check whether the step relies on any premise (assumption, bound,
edge case, or condition) that is not already present in the
previous state or the problem text. If you can identify such an
unstated premise, reject the step — the proof must make all
premises explicit before using them. Pay special attention to edge
cases the computation might silently exclude.

Accept ONLY if the computation is correct AND introduces no hidden
premises. Reject if the math is wrong, the step depends on a hidden
assumption, or the computation silently excludes valid edge cases.

When rejecting, exhaustively list every issue you find with the
step as a separately numbered point. Don't stop at the first error
or issue — enumerate all of them.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 3 being judged:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']
  Justification type: computation
  Justification: The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.

reasoning

{
 "summary": [
  "**Evaluating output requirements**\n\nI need to ensure the output is in the exact JSON schema. I’m thinking about the judging logic, noting that previous discussions mention a positive result requires published measurements from at least three labs with certified targets and uncertainties. Since Collins doesn't report measurements and uncertainty budgets from three labs, this study doesn't satisfy that condition. I need to acknowledge that the lack of reporting from three independent laboratories is a critical factor here—no hidden assumptions."
 ]
}

output

{
 "accepted": true,
 "reason": "The inference is valid: the stated condition is conjunctive and requires measurements with uncertainty information from at least three independent laboratories covering all four quantities. The previous state explicitly says Collins et al. do not report such three-laboratory measurements and uncertainty budgets, so that study cannot satisfy the condition. No new premise or excluded edge case is introduced."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the code interpreter (Python; sympy/numpy/scipy available) to recompute rather than trusting arithmetic.

You write one standalone SageMath program that independently recomputes a
single proof step. An engine — not you — produces the official result: it
saves your program as a `.sage` file and runs it with `sage <file>` in a clean
process under a 120-second budget, and a separate analyst compares the printed
output against the step's claim. You may draft and test in your own sandbox,
but only the returned program matters.

# Goal
A short, self-contained Sage program that recomputes the step's
BEFORE -> AFTER transformation from the BEFORE state and the justification
alone, and prints the recomputed result. The preparser is active (`^` is
exponentiation, integer literals are exact Integers) and the full Sage
library is available — symbolics, number theory, PARI/GP, GAP, Singular,
polyhedra, elliptic curves.

# Success criteria
- The program derives the result. It never hardcodes, copies, or pattern-matches
  the AFTER state or the proof's answer into what it prints — a reader of the
  code must see the claimed computation actually performed.
- Printed output is small and directly comparable to the step's claim: exact
  values (rationals/symbolics, not floats) unless the step itself is
  approximate.
- Deterministic: no input(), no network, no files, no randomness, no
  environment dependence.
- Terminates well within 120 seconds (interpreter startup already costs a few
  of them — keep the computation itself modest).

# If the step is not mechanically recomputable
When the step is not something a program can decide (it needs judgment or facts
outside the BEFORE state), return a program whose only effect is
`raise SystemExit("not mechanically recomputable: <one-line reason>")`.
A nonzero exit is recorded as "no grounding" — it never counts against the
proof, so never force a dubious computation just to print something.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 3 to ground:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']
  Justification type: computation
  Justification: The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.

output

{
 "code": "required_quantities = Set([\"resolution\", \"field_curvature\", \"illumination_uniformity\", \"stage_repeatability\"])\n\ncollins_evidence = {\n    \"independent_laboratories\": 1,\n    \"quantitatively_measured\": Set([\"resolution\"]),\n    \"certified_targets_for_all_quantities\": False,\n    \"stated_uncertainties_for_comparison\": False\n}\n\ncondition_satisfied = (\n    collins_evidence[\"independent_laboratories\"] >= 3\n    and required_quantities.issubset(collins_evidence[\"quantitatively_measured\"])\n    and collins_evidence[\"certified_targets_for_all_quantities\"]\n    and collins_evidence[\"stated_uncertainties_for_comparison\"]\n)\n\nprint(condition_satisfied)\n"
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You are auditing step 4 of a proof generated by an LLM.
LLMs hallucinate facts, citations, definitions, and reasoning. Your
job is specifically to FIND ERRORS, not to confirm what looks
plausible. Treat every claim with skepticism.

The step claims this transformation is justified by a theorem, law,
identity, or definition:
  BEFORE: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']
  AFTER:  ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']
  CITED:  The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))

Decide: does the cited result exist, is it applied correctly here,
and does it justify every change from BEFORE to AFTER?

Verify by web search rather than plausibility or recall, in
particular:
- Introduced definitions ("X is defined as ..."): confirm the
  definition matches the canonical published source — the LLM may
  present one component of a multi-part definition as the whole
  thing.
- Steps that seem too basic to cite: even a move like "let x = ..."
  has a real underlying justification (definitional extension, a
  foundational rule of logic). Confirm the implicit foundational
  rule is real and correctly applied; do not reject a step just
  because its justification feels trivial.
- Specific factual claims you cannot derive by general reasoning:
  if you cannot verify such a claim after searching, reject the
  step.

Check whether the step relies on any premise (assumption, bound,
edge case, or factual claim) that is not already present in the
previous state or the problem text. If you can identify such an
unstated premise, reject the step — the proof must make all
premises explicit before using them.

Accept if the citation (or underlying justification) is real and
correctly applied, AND the step introduces no hidden premises.
Reject if the cited result doesn't exist, doesn't apply, doesn't
account for all changes in the state, smuggles in an unjustified
claim, or relies on a hidden premise.

When rejecting, exhaustively list every issue you find with the
step as a separately numbered point. Don't stop at the first error
or issue — enumerate all of them.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 4 being judged:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']
  Justification type: citation
  Justification: The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://eprints.gla.ac.uk/327438/2/327438.pdf"
 }
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "Knapper Developing the OpenFlexure Microscope towards medical use calibration MICAT USAF 1951 illumination camera calibration stage-to-image calibration",
   "site:royalsocietypublishing.org rsta.2023.0257 Knapper OpenFlexure calibration data accessibility no additional data",
   "\"MICAT\" \"OpenFlexure\" resolution calibration"
  ],
  "query": "Knapper Developing the OpenFlexure Microscope towards medical use calibration MICAT USAF 1951 illumination camera calibration stage-to-image calibration"
 }
}

reasoning

{
 "summary": [
  "**Verifying data accessibility**\n\nI need to ensure that I can verify the data accessibility accurately. My first step is to explore the PMC to find the necessary information. It's important to double-check everything to avoid any issues later on. I'll take my time to gather the right data and ensure I fully understand what's accessible. By doing this, I can provide the best possible support and answers when needed."
 ]
}

web_search

{
 "action": {
  "pattern": "Data accessibility",
  "type": "find_in_page",
  "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC11448745/"
 }
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "\"This article has no additional data\" \"OpenFlexure\"",
   "\"Data accessibility\" \"Developing the OpenFlexure Microscope towards medical use\"",
   "\"article has no additional data\" Knapper Whiteford Rosen OpenFlexure",
   "site:royalsocietypublishing.org/doi/10.1098/rsta.2023.0257 \"Data accessibility\""
  ],
  "query": "\"This article has no additional data\" \"OpenFlexure\""
 }
}

output

{
 "accepted": true,
 "reason": "The cited paper exists and supports every added claim: it describes calibration/self-certification procedures, states that illumination and camera-sensor calibration can be performed without a sample, describes stage-to-image calibration, identifies MICAT’s use of a USAF 1951 target for resolution and physical-distance calibration, and states, “This article has no additional data.” The added sentence accurately summarizes these procedures as a workflow and introduces no hidden premise. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf?utm_source=openai))"
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You name the one best source where a cited mathematical result can be read.
You do NOT quote from it — the engine will fetch the page itself, and a
separate agent will extract quotes from exactly what the engine receives.
Your only job is a good URL.

# Goal
The step invokes a named theorem, law, identity, or definition. Return:
- `url` — where the canonical statement can be read. The engine's fetcher is
  plain HTTP: the page must be publicly fetchable static HTML or plain text —
  no paywalls, no login, no JavaScript-rendered content. Prefer reference
  pages (Wikipedia, ProofWiki article pages, published lecture notes). One
  authoritative fetchable source is enough.
- `note` — one sentence: what you expect the page to state that licenses
  this step.

# If no fetchable source exists
Return `url: ""` with the note explaining what you looked for. An unnamed
source is a harmless no-op — never invent a URL that might not exist.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 4 to ground:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']
  Justification type: citation
  Justification: The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "site:royalsocietypublishing.org/doi/full/10.1098/rsta.2023.0257 Developing the OpenFlexure Microscope towards medical use calibration USAF 1951 data accessibility",
   "10.1098/rsta.2023.0257 full text HTML"
  ],
  "query": "site:royalsocietypublishing.org/doi/full/10.1098/rsta.2023.0257 Developing the OpenFlexure Microscope towards medical use calibration USAF 1951 data accessibility"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC11168677/"
 }
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "\"Developing the OpenFlexure Microscope towards medical use\" PMC",
   "\"Developing the OpenFlexure Microscope towards medical use\" html",
   "\"MICAT\" \"USAF 1951\" OpenFlexure Knapper"
  ],
  "query": "\"Developing the OpenFlexure Microscope towards medical use\" PMC"
 }
}

reasoning

{
 "summary": [
  "**Ensuring HTML quality**\n\nI'm focusing on creating the best static HTML for the PMC. I need to ensure that each line includes necessary data statements and proper calibration. It's also important that this HTML is open, perhaps even searchable, so users can easily find what they need. These details matter a lot to make sure the final product meets expectations! Let’s keep refining it until it's just right for the end users."
 ]
}

web_search

{
 "action": {
  "pattern": "Data accessibility",
  "type": "find_in_page",
  "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC11448745/"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11448745/"
 }
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11448745/"
 }
}

reasoning

{
 "summary": [
  "**Finalizing JSON format**\n\nI need to ensure I have the final JSON in the correct format. The URL might be from www.ncbi.nlm.nih.gov, which typically handles plain HTTP redirects well, but I might also consider using a direct pmc URL, despite the occasional reCAPTCHA. The user mentioned that the engine is plain HTTP, which could work. NCBI's static URLs are likely acceptable, and I might also want to check EuropePMC for static options. I'll search and then open the exact link."
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "site:europepmc.org/articles/PMC11448745 \"Data accessibility\"",
   "site:europepmc.org/article/MED/38826050 OpenFlexure Knapper"
  ],
  "query": "site:europepmc.org/articles/PMC11448745 \"Data accessibility\""
 }
}

output

{
 "url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11448745/",
 "note": "The full-text article’s calibration section describes illumination/camera and stage-to-image calibration plus MICAT resolution calibration using a USAF 1951 target, and its data-accessibility statement says there are no additional data."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the code interpreter (Python; sympy/numpy/scipy available) to recompute rather than trusting arithmetic.

You are auditing step 5 of a proof generated by an LLM.
LLMs hallucinate and make subtle math errors that look correct on
a casual read. Your job is specifically to FIND ERRORS. Recompute
everything from scratch — do not trust the LLM's arithmetic or
algebra.

The step claims this is a correct computation:
  BEFORE: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']
  AFTER:  ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  CLAIM:  A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.

Verify the math by recomputing it yourself.

Check whether the step relies on any premise (assumption, bound,
edge case, or condition) that is not already present in the
previous state or the problem text. If you can identify such an
unstated premise, reject the step — the proof must make all
premises explicit before using them. Pay special attention to edge
cases the computation might silently exclude.

Accept ONLY if the computation is correct AND introduces no hidden
premises. Reject if the math is wrong, the step depends on a hidden
assumption, or the computation silently excludes valid edge cases.

When rejecting, exhaustively list every issue you find with the
step as a separately numbered point. Don't stop at the first error
or issue — enumerate all of them.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 5 being judged:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  Justification type: computation
  Justification: A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.

reasoning

{
 "summary": [
  "**Evaluating dataset accessibility**\n\nI'm trying to understand if I can establish that no dataset is available. The standard accessibility statement suggests there’s no associated data, but there could be comparative data in the article. I might be making a hidden assumption! I need to clearly outline everything, separately numbered, without involving math. I’m also considering that the USAF target may not be certified. However, the conclusion still claims there’s no dataset. Even if the logic seems valid conditionally, the foundational assumption isn’t there. I'll need to clarify specific citations regarding calibration and accessibility. I’ll need exact boolean reasoning for that."
 ]
}

output

{
 "accepted": false,
 "reason": "1. The step assumes Knapper et al. contain no comparative three-laboratory data, but the previous state establishes only that the paper describes a calibration workflow and says there are “no additional data.” A data-accessibility statement of that kind does not imply that no comparative measurements are reported within the article itself.\n2. The previous state does not explicitly establish that its summary of Knapper et al. is exhaustive. Listing several calibration procedures does not by itself rule out a three-laboratory dataset elsewhere in the paper.\n3. Therefore, although the conditional claim that a workflow without comparative data cannot establish interlaboratory agreement is logically correct, the required antecedent—absence of comparative laboratory data—has not been established in the previous state."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the code interpreter (Python; sympy/numpy/scipy available) to recompute rather than trusting arithmetic.

You write one standalone SageMath program that independently recomputes a
single proof step. An engine — not you — produces the official result: it
saves your program as a `.sage` file and runs it with `sage <file>` in a clean
process under a 120-second budget, and a separate analyst compares the printed
output against the step's claim. You may draft and test in your own sandbox,
but only the returned program matters.

# Goal
A short, self-contained Sage program that recomputes the step's
BEFORE -> AFTER transformation from the BEFORE state and the justification
alone, and prints the recomputed result. The preparser is active (`^` is
exponentiation, integer literals are exact Integers) and the full Sage
library is available — symbolics, number theory, PARI/GP, GAP, Singular,
polyhedra, elliptic curves.

# Success criteria
- The program derives the result. It never hardcodes, copies, or pattern-matches
  the AFTER state or the proof's answer into what it prints — a reader of the
  code must see the claimed computation actually performed.
- Printed output is small and directly comparable to the step's claim: exact
  values (rationals/symbolics, not floats) unless the step itself is
  approximate.
- Deterministic: no input(), no network, no files, no randomness, no
  environment dependence.
- Terminates well within 120 seconds (interpreter startup already costs a few
  of them — keep the computation itself modest).

# If the step is not mechanically recomputable
When the step is not something a program can decide (it needs judgment or facts
outside the BEFORE state), return a program whose only effect is
`raise SystemExit("not mechanically recomputable: <one-line reason>")`.
A nonzero exit is recorded as "no grounding" — it never counts against the
proof, so never force a dubious computation just to print something.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 5 to ground:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  Justification type: computation
  Justification: A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.

output

{
 "code": "raise SystemExit(\"not mechanically recomputable: the step is a qualitative inference from prose about evidentiary sufficiency, not a formal computation derivable from structured data\")"
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You are auditing step 6 of a proof generated by an LLM.
LLMs hallucinate facts, citations, definitions, and reasoning. Your
job is specifically to FIND ERRORS, not to confirm what looks
plausible. Treat every claim with skepticism.

The step claims this transformation is justified by a theorem, law,
identity, or definition:
  BEFORE: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  AFTER:  ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  CITED:  Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))

Decide: does the cited result exist, is it applied correctly here,
and does it justify every change from BEFORE to AFTER?

Verify by web search rather than plausibility or recall, in
particular:
- Introduced definitions ("X is defined as ..."): confirm the
  definition matches the canonical published source — the LLM may
  present one component of a multi-part definition as the whole
  thing.
- Steps that seem too basic to cite: even a move like "let x = ..."
  has a real underlying justification (definitional extension, a
  foundational rule of logic). Confirm the implicit foundational
  rule is real and correctly applied; do not reject a step just
  because its justification feels trivial.
- Specific factual claims you cannot derive by general reasoning:
  if you cannot verify such a claim after searching, reject the
  step.

Check whether the step relies on any premise (assumption, bound,
edge case, or factual claim) that is not already present in the
previous state or the problem text. If you can identify such an
unstated premise, reject the step — the proof must make all
premises explicit before using them.

Accept if the citation (or underlying justification) is real and
correctly applied, AND the step introduces no hidden premises.
Reject if the cited result doesn't exist, doesn't apply, doesn't
account for all changes in the state, smuggles in an unjustified
claim, or relies on a hidden premise.

When rejecting, exhaustively list every issue you find with the
step as a separately numbered point. Don't stop at the first error
or issue — enumerate all of them.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 6 being judged:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  Justification type: citation
  Justification: Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))

reasoning

{
 "summary": [
  "**Auditing claims**\n\nI need to carefully audit the exact claim, which means I should browse a specific catalogue. I’ll inspect the documents through 2026 and check if they have a peer-reviewed distinction. Alright, so I might need to search the web for relevant pages to support this. I realize this could take some time, but it's important to get this right! Let’s see what I can find that meets these criteria."
 ]
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://openflexure.gitlab.io/about/publications"
 }
}

reasoning

{
 "summary": [
  "**Deciding on catalogue entries**\n\nI need to decide whether to reject a submission based on a catalogue that isn’t comprehensive. Just because something isn’t listed doesn’t mean there’s no peer-reviewed entry. The claim is that the catalogue lacks entries, which I can verify against the list. It’s tricky because the publications are current only until 2026, but many projects stop at 2024. I’ll need to closely inspect individual titles to ensure nothing is overlooked. Plus, the lack of peer-reviewed entries might be resolved through title screening or searching for specific papers."
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "site:openflexure.gitlab.io/about/publications OpenFlexure interlaboratory three laboratories metrology resolution field curvature illumination stage repeatability",
   "OpenFlexure microscope interlaboratory comparison resolution field curvature illumination uniformity stage repeatability uncertainty",
   "OpenFlexure microscope three laboratories calibration uncertainty repeatability",
   "OpenFlexure publications 2026 microscope metrology comparison"
  ],
  "query": "site:openflexure.gitlab.io/about/publications OpenFlexure interlaboratory three laboratories metrology resolution field curvature illumination stage repeatability"
 }
}

reasoning

{
 "summary": [
  "**Reviewing claims on literature**\n\nI'm analyzing a narrow claim regarding a catalogue that says it \"contains no peer-reviewed entry,\" which I can verify from the page list itself. The phrase \"current through work listed for 2026\" only indicates that it includes 2026 entries, not that it's comprehensive. While it could be accepted as a catalogue absence, it’s also used to assert the lack of qualifying literature, adding just a factual note. The claim could be misleading overall due to the page’s nature.",
  "**Analyzing validity of claims**\n\nI'm considering the claim that a source \"contains no entry reporting...,\" which could come from checking the title list and conducting an external inspection, but the citation only points to the page itself. Additionally, it seems to suggest that all candidate entries are peer-reviewed, which might not be true. I need to clarify if a numbered, exhaustive reason is required. It’s also unclear if citations are necessary, especially since we parsed the data but didn't formally cite it. I must ensure the output is valid JSON."
 ]
}

output

{
 "accepted": false,
 "reason": "1. The catalogue is not represented as exhaustive. Its “Citing publications” section explicitly asks users to notify the project so publications can be added, so absence from this list cannot establish absence of a qualifying peer-reviewed study. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))\n2. “Current through work listed for 2026” is unsupported and misleading. The page lists two 2026 papers only under “Citing publications,” while the project’s own “Publications and conferences” list ends in 2024; inclusion of some 2026 citations does not demonstrate comprehensive coverage through August 31, 2026. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))\n3. The catalogue supplies mainly bibliographic entries and titles. It does not document that every listed paper was inspected for measurements from three laboratories, all four quantities, certified targets, and uncertainty budgets. Therefore it cannot by itself justify the detailed content-based negative claim.\n4. The page combines journal articles, conference papers, presentations, preprints, and citing publications, including an F1000Research item whose displayed peer-review status includes one approval and one non-approval. Thus the citation does not provide a clean, defined catalogue of exclusively peer-reviewed entries matching the claim’s characterization. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))"
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You name the one best source where a cited mathematical result can be read.
You do NOT quote from it — the engine will fetch the page itself, and a
separate agent will extract quotes from exactly what the engine receives.
Your only job is a good URL.

# Goal
The step invokes a named theorem, law, identity, or definition. Return:
- `url` — where the canonical statement can be read. The engine's fetcher is
  plain HTTP: the page must be publicly fetchable static HTML or plain text —
  no paywalls, no login, no JavaScript-rendered content. Prefer reference
  pages (Wikipedia, ProofWiki article pages, published lecture notes). One
  authoritative fetchable source is enough.
- `note` — one sentence: what you expect the page to state that licenses
  this step.

# If no fetchable source exists
Return `url: ""` with the note explaining what you looked for. An unnamed
source is a harmless no-op — never invent a URL that might not exist.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 6 to ground:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  Justification type: citation
  Justification: Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))

reasoning

{
 "summary": [
  "**Verifying URL accessibility**\n\nI need to ensure the output is in exact JSON format. It’s also important to verify that the user-supplied URL is fetchable, so I’ll need to check if it’s redirecting or current. I think searching the web for this might be a helpful step. Making sure everything is accurate and works smoothly is really crucial, and I want to get this right for the user. Let’s go ahead and check!"
 ]
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://openflexure.gitlab.io/about/publications"
 }
}

output

{
 "url": "https://openflexure.gitlab.io/about/publications",
 "note": "The OpenFlexure project’s publicly accessible publication catalogue lists its peer-reviewed outputs and citing publications through 2026, allowing verification that it contains no three-laboratory study jointly reporting the four specified metrological quantities with uncertainty budgets."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the code interpreter (Python; sympy/numpy/scipy available) to recompute rather than trusting arithmetic.

You are auditing step 7 of a proof generated by an LLM.
LLMs hallucinate and make subtle math errors that look correct on
a casual read. Your job is specifically to FIND ERRORS. Recompute
everything from scratch — do not trust the LLM's arithmetic or
algebra.

The step claims this is a correct computation:
  BEFORE: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  AFTER:  ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  CLAIM:  Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.

Verify the math by recomputing it yourself.

Check whether the step relies on any premise (assumption, bound,
edge case, or condition) that is not already present in the
previous state or the problem text. If you can identify such an
unstated premise, reject the step — the proof must make all
premises explicit before using them. Pay special attention to edge
cases the computation might silently exclude.

Accept ONLY if the computation is correct AND introduces no hidden
premises. Reject if the math is wrong, the step depends on a hidden
assumption, or the computation silently excludes valid edge cases.

When rejecting, exhaustively list every issue you find with the
step as a separately numbered point. Don't stop at the first error
or issue — enumerate all of them.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 7 being judged:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  Justification type: computation
  Justification: Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.

reasoning

{
 "summary": [
  "**Evaluating JSON requirements**\n\nI need to focus on the specifics of the JSON verdict. There's a date of August 31, 2026, mentioned, but it seems unstated in earlier context. It claims to represent current conditions for 2026 without specifying the date. There's a concern about stats from July 2026 and what constitutes the present measures. The evidence review says it's based on a catalog that might not be complete, and there’s ambiguity about the necessity of published measurements. The question hints at potential unpublished data's relevance, despite claiming a publication requirement that isn’t clear.",
  "**Clarifying logical structure**\n\nI think the principal characterization shouldn't restate \"neither.\" I need to ensure there's an exhaustive list. Another logical problem is that just because something is absent in the project catalog and two sources doesn’t mean it’s absent from all published evidence, unless the catalog is complete. The conclusion states that the \"published evidence reviewed does not meet...\" which is important. The catalog identifies nothing, but if the \"as of date\" is invalid, I need a clear, formatted reason with numbered points."
 ]
}

output

{
 "accepted": false,
 "reason": "1. The exact cutoff “as of August 31, 2026” is introduced without support. The previous state says only that the catalogue is current through work listed for 2026; it does not establish that the catalogue was checked or complete specifically on August 31, 2026. The undated inference that the reviewed evidence does not establish the required agreement is valid, but attaching this precise date requires an additional explicit premise."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the code interpreter (Python; sympy/numpy/scipy available) to recompute rather than trusting arithmetic.

You write one standalone SageMath program that independently recomputes a
single proof step. An engine — not you — produces the official result: it
saves your program as a `.sage` file and runs it with `sage <file>` in a clean
process under a 120-second budget, and a separate analyst compares the printed
output against the step's claim. You may draft and test in your own sandbox,
but only the returned program matters.

# Goal
A short, self-contained Sage program that recomputes the step's
BEFORE -> AFTER transformation from the BEFORE state and the justification
alone, and prints the recomputed result. The preparser is active (`^` is
exponentiation, integer literals are exact Integers) and the full Sage
library is available — symbolics, number theory, PARI/GP, GAP, Singular,
polyhedra, elliptic curves.

# Success criteria
- The program derives the result. It never hardcodes, copies, or pattern-matches
  the AFTER state or the proof's answer into what it prints — a reader of the
  code must see the claimed computation actually performed.
- Printed output is small and directly comparable to the step's claim: exact
  values (rationals/symbolics, not floats) unless the step itself is
  approximate.
- Deterministic: no input(), no network, no files, no randomness, no
  environment dependence.
- Terminates well within 120 seconds (interpreter startup already costs a few
  of them — keep the computation itself modest).

# If the step is not mechanically recomputable
When the step is not something a program can decide (it needs judgment or facts
outside the BEFORE state), return a program whose only effect is
`raise SystemExit("not mechanically recomputable: <one-line reason>")`.
A nonzero exit is recorded as "no grounding" — it never counts against the
proof, so never force a dubious computation just to print something.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 7 to ground:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  Justification type: computation
  Justification: Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.

output

{
 "code": "raise SystemExit(\"not mechanically recomputable: the conclusion depends on interpreting externally cited publications and a catalogue, not on decidable data contained in the BEFORE state\")"
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the code interpreter (Python; sympy/numpy/scipy available) to recompute rather than trusting arithmetic.

You are auditing step 8 of a proof generated by an LLM.
LLMs hallucinate and make subtle math errors that look correct on
a casual read. Your job is specifically to FIND ERRORS. Recompute
everything from scratch — do not trust the LLM's arithmetic or
algebra.

The step claims this is a correct computation:
  BEFORE: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  AFTER:  ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  CLAIM:  Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Verify the math by recomputing it yourself.

Check whether the step relies on any premise (assumption, bound,
edge case, or condition) that is not already present in the
previous state or the problem text. If you can identify such an
unstated premise, reject the step — the proof must make all
premises explicit before using them. Pay special attention to edge
cases the computation might silently exclude.

Accept ONLY if the computation is correct AND introduces no hidden
premises. Reject if the math is wrong, the step depends on a hidden
assumption, or the computation silently excludes valid edge cases.

When rejecting, exhaustively list every issue you find with the
step as a separately numbered point. Don't stop at the first error
or issue — enumerate all of them.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 8 being judged:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  New state: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  Justification type: computation
  Justification: Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

reasoning

{
 "summary": [
  "**Ensuring logical structure**\n\nI’m thinking about establishing the importance of providing evidence in a concise manner. It seems clear that when analyzing a local logical step, I need to focus on a JSON boolean format for clarity. I must ensure that it adheres to the exact schema without any extras. This will help maintain a tight structure and clear understanding, which I think is essential for effective communication. I’m making note of these details!"
 ]
}

output

{
 "accepted": true,
 "reason": "The step correctly converts the established failure of the necessary evidentiary condition into the epistemic conclusion “not demonstrated,” while explicitly avoiding the invalid inference that the laboratories actually disagree. It introduces no new premise beyond the previous state."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the code interpreter (Python; sympy/numpy/scipy available) to recompute rather than trusting arithmetic.

You write one standalone SageMath program that independently recomputes a
single proof step. An engine — not you — produces the official result: it
saves your program as a `.sage` file and runs it with `sage <file>` in a clean
process under a 120-second budget, and a separate analyst compares the printed
output against the step's claim. You may draft and test in your own sandbox,
but only the returned program matters.

# Goal
A short, self-contained Sage program that recomputes the step's
BEFORE -> AFTER transformation from the BEFORE state and the justification
alone, and prints the recomputed result. The preparser is active (`^` is
exponentiation, integer literals are exact Integers) and the full Sage
library is available — symbolics, number theory, PARI/GP, GAP, Singular,
polyhedra, elliptic curves.

# Success criteria
- The program derives the result. It never hardcodes, copies, or pattern-matches
  the AFTER state or the proof's answer into what it prints — a reader of the
  code must see the claimed computation actually performed.
- Printed output is small and directly comparable to the step's claim: exact
  values (rationals/symbolics, not floats) unless the step itself is
  approximate.
- Deterministic: no input(), no network, no files, no randomness, no
  environment dependence.
- Terminates well within 120 seconds (interpreter startup already costs a few
  of them — keep the computation itself modest).

# If the step is not mechanically recomputable
When the step is not something a program can decide (it needs judgment or facts
outside the BEFORE state), return a program whose only effect is
`raise SystemExit("not mechanically recomputable: <one-line reason>")`.
A nonzero exit is recorded as "no grounding" — it never counts against the
proof, so never force a dubious computation just to print something.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 8 to ground:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  New state: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  Justification type: computation
  Justification: Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

reasoning

{
 "summary": [
  "**Evaluating response format**\n\nI’m thinking about the necessity of justifying the approach. It seems like hardcoding isn’t needed, and using labels might be acceptable. I also need to ensure that the returned format is JSON because the response format specifies a code string. Considering that the program is likely expecting a specific format, I really need to focus on producing the correct JSON structure in the response. That’s essential!"
 ]
}

output

{
 "code": "# Propositions:\n# E: the necessary evidentiary condition is met\n# D: the claimed interlaboratory agreement is demonstrated\n# X: the laboratories actually disagree\n#\n# Previous state gives not E. The justification gives D => E.\n\nmodels = []\nfor E in [False, True]:\n    for D in [False, True]:\n        for X in [False, True]:\n            if ((not D) or E) and (not E):\n                models.append((E, D, X))\n\ndef forced_value(index):\n    values = Set(model[index] for model in models)\n    if values == Set([True]):\n        return True\n    if values == Set([False]):\n        return False\n    return \"undetermined\"\n\nprint(\"agreement demonstrated:\", forced_value(1))\nprint(\"laboratories disagree:\", forced_value(2))"
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You are the contradiction check on a deterministic grounding. An independent
agent produced an artifact for one proof step (a sympy program, a Lean file,
or a source extraction); the ENGINE then executed or verified it first-hand.
You see the artifact and the engine-witnessed output, and return a verdict
only — never fixes, never advice.

Your verdict gates a hard rejection: `accepted: false` cannot be overturned
downstream, so it must mean a genuine, demonstrated contradiction.

# Decide

Reject (`accepted: false`) only when BOTH hold:
1. The artifact faithfully checks what the step claims — same quantities, same
   relation, computed rather than copied; a checked Lean statement says what
   the step says; verified quotes are about the fact the step relies on.
2. The engine-witnessed output contradicts the step's claimed transformation —
   a different value, a failed relation, a checked Lean statement proving the
   NEGATION of the step's claim, or source text that states something
   incompatible with what the step attributes to it. A proved negation counts
   as faithful for criterion 1: it addresses exactly the step's claim.

Everything else accepts (`accepted: true`), because acceptance is the neutral
outcome — the step still faces its own judge:
- Representation differences are NOT contradictions: 2/4 vs 1/2, sqrt(2)/2 vs
  1/sqrt(2), reordered terms, equivalent phrasing, print formatting.
- An artifact that is not probative — it hardcodes the answer, computes
  something other than the step's claim, states a weaker/stronger theorem, or
  quotes text unrelated to the claim — accepts, with a reason saying the
  grounding was not probative.
- Output you cannot decisively map onto the step's claim accepts.

For extraction groundings, the output lists the fetched source (url + sha256
provenance header) and each quote's alignment: status, char interval, and the
aligned source span. Judge from the SPAN text — that is the source's own
wording, engine-witnessed; the author's quote is only the search key. A
MATCH_FUZZY span whose actual wording states something incompatible with what
the step attributes to the source is exactly the contradiction to reject.

# Reason field
One or two sentences. On rejection, quote the engine-witnessed output verbatim
against the step's claimed value — the repair loop sees only your reason, so
the deterministic evidence must be in it. On acceptance, say what the grounding
established (or why it was not probative). Verdict only: never suggest how to
fix the step.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Step 1 whose grounding is under review:
  Previous state: ['ANSWER']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  Justification type: problem_given
  Justification: This is the conjunctive evidentiary requirement stated in the question.

Artifact (produced by an independent grounding agent):
The quote makes agreement a conjunctive requirement covering all four named quantities, certified targets, three independent laboratories, and stated uncertainties. It does not explicitly require the measurements to be published, so that part of the new state is not grounded in the problem statement.
quote 1 (author): 'resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties'

Engine-witnessed output:
source: problem statement
quote 1: MATCH_EXACT [35..214] 'resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties'

output

{
 "accepted": false,
 "reason": "The engine-witnessed problem statement says only “resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties”; it does not state the added requirement that the measurements be published."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You extract the exact source text a proof step rests on — FROM THE PAGE TEXT
PROVIDED IN THE PROMPT. The engine fetched that text itself and will align
every quote you return against exactly those bytes, token-by-token (bounded
tolerance for whitespace, casing, and typographic punctuation — never
paraphrase, never quote from memory). A separate analyst then judges whether
the engine-verified spans actually license the step.

# Goal
From the provided page text, put in `quotes` the substring(s) that state the
result the step invokes, copied from the page text as-is.

`claim_mapping`: one or two sentences on how the quotes license this step's
BEFORE -> AFTER transformation — including what they do NOT cover, if the
justification claims more than the source states.

# Success criteria
- Every quote is copied from the provided text, not composed or recalled.
- Quotes are the minimal spans that state the relied-on fact — not whole
  paragraphs, not fragments too short to assert anything. Prefer plain-prose
  statements; avoid regions mangled by leftover markup.
- If a multi-part theorem is involved, quote enough that cherry-picking
  would be visible.

# If the page does not state it
If the provided text does not contain what the step attributes to the
source, return your best honest extraction anyway (the nearest relevant
passage) and say in `claim_mapping` that it does not support the claim — the
analyst, not you, decides whether that is a contradiction.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Step 6 whose citation needs quoting:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  Justification: Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))

Source page (fetched by the engine from https://openflexure.gitlab.io/about/publications):
---


  

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Peer-Reviewed Research and Conference Papers

        
        

          
A collection of journal articles, conference papers, and other scholarly outputs produced through the OpenFlexure project and its international research collaborations.


        



    

  



 
  

    

      

        

           

  
If you’ve used our work, please consider citing the most relevant papers below, or our 2020 Robotic microscopy for everyone paper as:
Collins, J.T. et al. (2020) “Robotic Microscopy for everyone: The OpenFlexure Microscope”, Biomedical Optics Express, 11(5), p. 2447. doi:10.1364/boe.385729.





Publications and conferences



The work of the OpenFlexure project has been published in scientific journals and presented at conferences.




  
  

    
     Developing the OpenFlexure Microscope towards medical use: technical and social challenges of developing globally accessible hardware for healthcare 
     
    
      Philosophical Transactions of the Royal Society A  ·  2024
    
     
  

  
  

    
     Utility of a low-cost 3-D printed microscope for evaluating esophageal biopsies 
     
    
      Annals of 3D Printed Medicine  ·  2024
    
     
  

  
  

    
     Controlling and scripting laboratory hardware with open-source, intuitive interfaces: OpenFlexure Voice Control and OpenFlexure Blockly 
     
    
      Royal Society Open Science  ·  2023
    
     
    
       [
        arXiv ]  
    
    
  

  
  

    
     Multi-modal microscopy imaging with the OpenFlexure Delta Stage 
     
    
      Optics Express  ·  2022
    
     
    
       [
        arXiv ]  
    
    
  

  
  

    
     Simplifying the OpenFlexure Microscope software with the web of things 
     
    
      Royal Society Open Science  ·  2021
    
     
  

  
  

    
     Fast, high precision autofocus on a motorised microscope: automating blood sample imaging on the OpenFlexure Microscope 
     
    
      Journal of Microscopy  ·  2021
    
     
  

  
  

    
     HardOps: Utilising the software development toolchain for hardware design 
     
    
      International Journal of Computer Integrated Manufacturing  ·  2021
    
     
    
       [
        TechRxiv ]  
    
    
  

  
  

    
     An Open‐Source Modular Framework for Automated Pipetting and Imaging Applications 
     
    
      Advanced Biology  ·  2021
    
     
  

  
  

    
     Transitioning from Academic Innovation to Viable Humanitarian Technology: The Next Steps for the OpenFlexure Project 
     
    
      IST-Africa conference  ·  2021
    
     
  

  
  

    
     Low-cost, multimodal bioimaging with the OpenFlexure Delta Stage Microscope 
     
    
      RMS Frontiers in Bioimaging  ·  2020
    
     
  

  
  

    
     The OpenFlexure Project. The technical challenges of Co-Developing a microscope in the UK and Tanzania 
     
    
      IEEE Global Humanitarian Technology Conference (GHTC)  ·  2020
    
     
    
       [
        AfricaArXiv ]  
    
    
  

  
  

    
     Robotic microscopy for everyone: the OpenFlexure Microscope 
     
    
      Biomedical Optics Express  ·  2020
    
     
    
       [
        bioRxiv ]   🏆
       Best paper prize 
      
    
    
  

  
  

    
     The OpenFlexure Block Stage: sub-100 nm fibre alignment with a monolithic plastic flexure stage 
     
    
      Optics Express  ·  2020
    
     
  

  
  

    
     Flat-Field and Colour Correction for the Raspberry Pi Camera Module 
     
    
      Journal of Open Hardware  ·  2020
    
     
  

  
  

    
     A one-piece 3D printed flexure translation stage for open-source microscopy 
     
    
      Review of Scientific Instruments  ·  2016
    
     
  

  




Citing publications



The OpenFlexure project is now used and cited by a growing number of academic publications. If you have used the designs in your work, please let us know and we’ll add you to the list below.




  
Srivastava, J., Curd, M. E., Yao, Y., Holroyd, N. J. H., Shanthraj, P., Singh, S. B., Mandal, S., Prangnell, P. B. and Burnett, T. L. Effect of quench- and age-induced grain boundary η-phase precipitates on hydrogen environmentally induced cracking (H-EIC) behaviour of AA7085 alloy in humid air. Journal of Materials Science. (2026)

  
Vázquez-Cisneros G, Zambrano-Gutierrez DF, Duque-Gimenez GC, Flores-Mayorga A, Zárate-Triviño DG, Rodríguez-Padilla C, Bedolla MA, Menchaca JL, Avina-Cervantes JG, Rodríguez-Nieto M. Integrated Study of Morphology and Viscoelastic Properties in the MG-63 Cancer Cell Line Technologies. 14(1): 60 (2026)

  
Srivastava, J., Curd, M. E., Euesden, R., Yao, Y., Garner, A., Singh, S. B., Mandal, S., Burnett, T. L. and Prangnell, P. B. The influence of partially recrystallized grain structures on hydrogen-environmentally induced cracking (H-EIC) behavior of AA7085 alloy in humid air. Corrosion Science, 256: 113199 (2025)

  
Stancu G. Best Harvest Moment for Colon Cancer Cells From 2D Cultures for 3D Tumoroid Bioprinting: An Experimental Observational Study. Cureus 17(10): e94367 (2025)

  
Choudhury, D., Dolezal, J. M., Dyer, E., Kochanny, S., Ramesh, S., Howard, F. M., Margalus, J. R., Schroeder, A., Schulte, J., Garassino, M. C., Kather, J. N., & Pearson, A. T. Developing a low-cost, open-source, locally manufactured workstation and computational pipeline for automated histopathology evaluation using deep learning EBioMedicine, 107: 105276. (2024)

  
Jay Christopher, Rebecca Craig, Rebecca E. McHugh, Andrew J. Roe, Ralf Bauer, Brian Patton, Gail McConnell, Liam M. Rooney, A 3D-printed optical microscope for low-cost histological imaging, Journal of Microscopy, 298(3), pp. 274–282 (2025)

  
P. Thongtade and W. Pora, Development of an Autoscan Motorized Microscope Utilizing the OpenFlexure Architecture ECTI-CON, Thailand, (2024)

  
Sven Schulze, Kumar Arumugam, Stephan Schlamminger, Ryan Fitzgerald, R Michael Verkouteren, René Theska and Gordon Shaw, Development of a high precision electrostatic force balance for measuring quantity of dispensed fluid as a new calibration standard for the becquerel, Meas. Sci. Technol. 35: 085020 (2024)

  
Koki Uebo, Yuto Shiokawa, Ryunosuke Takahashi, Suguru Nakata and Hiroki Wadati Development of a magneto-optical Kerr microscope using a 3D printer [version 2; peer review: 1 approved, 1 not approved]. F1000Research, 12: 860 (2024)

  
Euesden, R. T., Aboura, Y., Garner, A. J., Jailin, T., Grant, C., Barrett, Z., Engel, C., Shanthraj, P., Holroyd, N. J. H., Prangnell, P. B., & Burnett, T. L. In-situ observation of environmentally assisted crack initiation and short crack growth behaviour of new-generation 7xxx series alloys in humid air. Corrosion Science, 216: 111051 (2023)

  
Mark Kristan Espejo Cabello and Jeremie E. De Guzman Utilization of accessible resources in the fabrication of an affordable, portable, high-resolution, 3D printed, digital microscope for Philippine diagnostic applications, PLoS Global Public Health 3(11): e0002070 (2023)

  
A. Reguilon, W. Bethard and E. Brekke A low-cost confocal microscope for the undergraduate lab, American Journal Physics 91(5): 404 (2023)

  
Tai The Diep, Sarah Helen Needs, Samuel Bizley, and Alexander D. Edwards Rapid Bacterial Motility Monitoring Using Inexpensive 3D-Printed OpenFlexure Microscopy Allows Microfluidic Antibiotic Susceptibility Testing Micromachines 13, no. 11: 1974 (2022)

  
T. Matsui and D. Fujiwara Optical sectioning robotic microscopy for everyone: the structured illumination microscope with the OpenFlexure stages, Opt. Express 30(13), pp. 23208-23216 (2022).

  
Bowen Chen, Max Nadeau, Ming Y. Lu, Jana Lipkova, and Faisal Mahmood Real Time, Point-of-Care Pathology Diagnosis via Embedded Deep Learning, a poster awarded the “best research” prize at Pathology Visions 2020


  
Stephen D. Grant, Kyle Richford, Heidi L. Burdett, David McKee and Brian R. Patton Low-cost, open-access quantitative phase imaging of algal cells using the transport of intensity equation Royal Society Open Science 7, 1 (2020)

  
Grant SD, Cairns GS, Wistuba J and Patton BR. Adapting the 3D-printed Openflexure microscope enables computational super-resolution imaging [version 1; peer review: 2 approved]. F1000Research 2019, 8:2003





Resources



If you’re planning on publishing based on our work, we’ve found it can be challenging to make the figures look as good as the microscope itself! We’ve built a set of resources to help show the optical path and components of the OpenFlexure Microscope.

 
        

      

    

  

  
  
    
  



  

    

      

        
      

      

        

          
The OpenFlexure project aims to make high precision mechanical positioning available to anyone with a 3D printer - for use in microscopes, micromanipulators, and more.

        

        

          
            

              
              
              
            

            

              
Forum

              
Ask questions, share projects, and discuss OpenFlexure with the community.

            

          
            

              
              
              
            

            

              
GitLab Repo

              
Source code, hardware designs, and issue tracking for OpenFlexure projects.

            

          
            

              
              
              
            

            

              
LinkedIn

              
News, collaborations, and updates from OpenFlexure.

            

          
            

              
              
              
            

            

              
YouTube

              
Introductory and demonstration videos about the OpenFlexure project.

            

          
            

              
              
              
            

            

              
Bluesky

              
Project updates, announcements, and highlights from the OpenFlexure team.

            

          
            

                chat_bubble 
 
            

            

              
Contact

              
Contact the OpenFlexure team for media enquiries, partnerships, or collaboration.

            



      

    

    

      

        


      

    

    

      

        

          2026 © OpenFlexure. Licensed under
          CC BY-SA 4.0
        

      

      

Privacy PolicyCode of Conduct


    

  



  
    
  



  
    
      
        
          
        
      
      
        
          
        
      
    
  
  

    

      

        


      

    

  

  

    
  




    
    
    
    
    
    
  


---

output

{
 "quotes": [
  "A collection of journal articles, conference papers, and other scholarly outputs produced through the OpenFlexure project and its international research collaborations.",
  "Developing the OpenFlexure Microscope towards medical use: technical and social challenges of developing globally accessible hardware for healthcare \n     \n    \n      Philosophical Transactions of the Royal Society A  ·  2024\n    \n     \n  \n\n  \n  \n\n    \n     Utility of a low-cost 3-D printed microscope for evaluating esophageal biopsies \n     \n    \n      Annals of 3D Printed Medicine  ·  2024\n    \n     \n  \n\n  \n  \n\n    \n     Controlling and scripting laboratory hardware with open-source, intuitive interfaces: OpenFlexure Voice Control and OpenFlexure Blockly \n     \n    \n      Royal Society Open Science  ·  2023\n    \n     \n    \n       [\n        arXiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     Multi-modal microscopy imaging with the OpenFlexure Delta Stage \n     \n    \n      Optics Express  ·  2022\n    \n     \n    \n       [\n        arXiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     Simplifying the OpenFlexure Microscope software with the web of things \n     \n    \n      Royal Society Open Science  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     Fast, high precision autofocus on a motorised microscope: automating blood sample imaging on the OpenFlexure Microscope \n     \n    \n      Journal of Microscopy  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     HardOps: Utilising the software development toolchain for hardware design \n     \n    \n      International Journal of Computer Integrated Manufacturing  ·  2021\n    \n     \n    \n       [\n        TechRxiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     An Open‐Source Modular Framework for Automated Pipetting and Imaging Applications \n     \n    \n      Advanced Biology  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     Transitioning from Academic Innovation to Viable Humanitarian Technology: The Next Steps for the OpenFlexure Project \n     \n    \n      IST-Africa conference  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     Low-cost, multimodal bioimaging with the OpenFlexure Delta Stage Microscope \n     \n    \n      RMS Frontiers in Bioimaging  ·  2020\n    \n     \n  \n\n  \n  \n\n    \n     The OpenFlexure Project. The technical challenges of Co-Developing a microscope in the UK and Tanzania \n     \n    \n      IEEE Global Humanitarian Technology Conference (GHTC)  ·  2020\n    \n     \n    \n       [\n        AfricaArXiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     Robotic microscopy for everyone: the OpenFlexure Microscope \n     \n    \n      Biomedical Optics Express  ·  2020\n    \n     \n    \n       [\n        bioRxiv ]   🏆\n       Best paper prize \n      \n    \n    \n  \n\n  \n  \n\n    \n     The OpenFlexure Block Stage: sub-100 nm fibre alignment with a monolithic plastic flexure stage \n     \n    \n      Optics Express  ·  2020\n    \n     \n  \n\n  \n  \n\n    \n     Flat-Field and Colour Correction for the Raspberry Pi Camera Module \n     \n    \n      Journal of Open Hardware  ·  2020\n    \n     \n  \n\n  \n  \n\n    \n     A one-piece 3D printed flexure translation stage for open-source microscopy \n     \n    \n      Review of Scientific Instruments  ·  2016",
  "Srivastava, J., Curd, M. E., Yao, Y., Holroyd, N. J. H., Shanthraj, P., Singh, S. B., Mandal, S., Prangnell, P. B. and Burnett, T. L. Effect of quench- and age-induced grain boundary η-phase precipitates on hydrogen environmentally induced cracking (H-EIC) behaviour of AA7085 alloy in humid air. Journal of Materials Science. (2026)"
 ],
 "claim_mapping": "The page characterizes itself as a collection of OpenFlexure scholarly outputs, lists its project publications, and separately includes citing work dated 2026; inspection of the displayed project-publication titles reveals no three-laboratory study jointly covering the four named quantities. The page does not explicitly state that no such study exists, that the catalogue is complete or current through 2026, or that the listed papers lack the specified measurements and uncertainty budgets, so those parts are inferences from the catalogue rather than source-stated facts."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You are a pedantry filter for a verified-reasoning pipeline. A judge
has rejected a step in a proof. Your job is to decide whether the
rejection is LEGITIMATE (the proof is actually wrong) or PEDANTIC
(the proof is correct, the judge demanded more rigor than necessary
for this kind of problem).

If ANY numbered issue in the rejection looks like it points to an
error an LLM could plausibly make that would lead to a legitimately
incorrect answer, mark it as is_pedantic=false. A step is pedantic
ONLY if EVERY issue listed is pedantic. The whole point is to catch
real errors; don't downgrade something that could be a hallucination,
arithmetic mistake, fabricated citation, or wrong fact.

Use web search if you need to verify whether a citation or factual
claim is real before deciding.

Be CONSERVATIVE — when in doubt, mark as legitimate (is_pedantic=
false). The system needs to catch real errors more than it needs
to push borderline cases through.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 1 being evaluated:
  Previous state: ['ANSWER']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  Justification type: problem_given
  Justification: This is the conjunctive evidentiary requirement stated in the question.

A judge rejected this step with the following reason:
1. The problem does not state that the measurements must be published; “published” is an added evidentiary premise.
2. The problem says “across three independent labs,” not “at least three independent laboratories.” Treating this as a minimum of three is an interpretation rather than a directly stated value.

Is this rejection legitimate (the proof is actually wrong) or pedantic (the proof is correct, the judge is being too strict)?

reasoning

{
 "summary": [
  "**Evaluating JSON schema and sources**\n\nI need to output the exact JSON schema and consider several issues, like whether unpublished evidence can be legitimate when answering the user’s question about measured agreement. The user's request implies a need for accessible, published evidence. If I suspect a plausible error from the model, I should validate that with a web search. However, given the logical wording, I might not need to do that right away since the phrasing seems clear."
 ]
}

output

{
 "is_pedantic": false,
 "reason": "The rejection is legitimate because Step 1 adds a substantive requirement that the measurements be published. The question asks whether the measurements agree, not merely whether published evidence demonstrates agreement; unpublished or otherwise available three-lab results could make the answer positive. Interpreting “across three” as “at least three” is harmless, but the added publication premise could lead to an incorrect negative answer."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You are a pedantry filter for a verified-reasoning pipeline. A judge
has rejected a step in a proof. Your job is to decide whether the
rejection is LEGITIMATE (the proof is actually wrong) or PEDANTIC
(the proof is correct, the judge demanded more rigor than necessary
for this kind of problem).

If ANY numbered issue in the rejection looks like it points to an
error an LLM could plausibly make that would lead to a legitimately
incorrect answer, mark it as is_pedantic=false. A step is pedantic
ONLY if EVERY issue listed is pedantic. The whole point is to catch
real errors; don't downgrade something that could be a hallucination,
arithmetic mistake, fabricated citation, or wrong fact.

Use web search if you need to verify whether a citation or factual
claim is real before deciding.

Be CONSERVATIVE — when in doubt, mark as legitimate (is_pedantic=
false). The system needs to catch real errors more than it needs
to push borderline cases through.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 7 being evaluated:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  Justification type: computation
  Justification: Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.

A judge rejected this step with the following reason:
1. The exact cutoff “as of August 31, 2026” is introduced without support. The previous state says only that the catalogue is current through work listed for 2026; it does not establish that the catalogue was checked or complete specifically on August 31, 2026. The undated inference that the reviewed evidence does not establish the required agreement is valid, but attaching this precise date requires an additional explicit premise.

Is this rejection legitimate (the proof is actually wrong) or pedantic (the proof is correct, the judge is being too strict)?

output

{
 "is_pedantic": true,
 "reason": "The substantive inference is valid: the reviewed sources do not establish the required three-laboratory agreement. “As of August 31, 2026” merely timestamps that evidence review using the applicable current date; it does not materially assert that the catalogue was formally certified complete on that date. Requiring an additional premise for the timestamp is therefore pedantic, especially since the conclusion is expressly limited to “the published evidence reviewed.”"
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You are a pedantry filter for a verified-reasoning pipeline. A judge
has rejected a step in a proof. Your job is to decide whether the
rejection is LEGITIMATE (the proof is actually wrong) or PEDANTIC
(the proof is correct, the judge demanded more rigor than necessary
for this kind of problem).

If ANY numbered issue in the rejection looks like it points to an
error an LLM could plausibly make that would lead to a legitimately
incorrect answer, mark it as is_pedantic=false. A step is pedantic
ONLY if EVERY issue listed is pedantic. The whole point is to catch
real errors; don't downgrade something that could be a hallucination,
arithmetic mistake, fabricated citation, or wrong fact.

Use web search if you need to verify whether a citation or factual
claim is real before deciding.

Be CONSERVATIVE — when in doubt, mark as legitimate (is_pedantic=
false). The system needs to catch real errors more than it needs
to push borderline cases through.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 5 being evaluated:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  Justification type: computation
  Justification: A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.

A judge rejected this step with the following reason:
1. The step assumes Knapper et al. contain no comparative three-laboratory data, but the previous state establishes only that the paper describes a calibration workflow and says there are “no additional data.” A data-accessibility statement of that kind does not imply that no comparative measurements are reported within the article itself.
2. The previous state does not explicitly establish that its summary of Knapper et al. is exhaustive. Listing several calibration procedures does not by itself rule out a three-laboratory dataset elsewhere in the paper.
3. Therefore, although the conditional claim that a workflow without comparative data cannot establish interlaboratory agreement is logically correct, the required antecedent—absence of comparative laboratory data—has not been established in the previous state.

Is this rejection legitimate (the proof is actually wrong) or pedantic (the proof is correct, the judge is being too strict)?

reasoning

{
 "summary": [
  "**Verifying paper contents**\n\nI need to ensure I deliver the JSON output exactly as required. It’s essential to assess the specific paper mentioned. I think I'll need to browse to find the official document to verify the details within Knapper's work. Searching for and opening the official paper will help make sure I'm accurate in providing the right information."
 ]
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://doi.org/10.1098/rsta.2023.0257"
 }
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "Knapper Developing the OpenFlexure Microscope towards medical use PDF three laboratories calibration data",
   "site:royalsocietypublishing.org/doi/full/10.1098/rsta.2023.0257 OpenFlexure three laboratory",
   "\"Developing the OpenFlexure Microscope towards medical use\" calibration"
  ],
  "query": "Knapper Developing the OpenFlexure Microscope towards medical use PDF three laboratories calibration data"
 }
}

reasoning

{
 "summary": [
  "**Evaluating logical conclusions**\n\nI’m thinking about the conclusion in step 5. It connects to the idea of a workflow, but the statement “they present this as a workflow” doesn’t rule out the presence of data. I wonder if an LLM might incorrectly assume there’s no data due to the phrasing. It seems like some instructions could make any issue look like a real error, leading to a misunderstanding. I’ll need to explore the entire article, possibly checking all sections for data figures related to the proof."
 ]
}

web_search

{
 "action": {
  "pattern": "Data accessibility",
  "type": "find_in_page",
  "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC11448745/"
 }
}

reasoning

{
 "summary": [
  "**Clarifying rejection legitimacy**\n\nI’m considering how we can say that a rejection is legitimate. It seems that just because a previous state doesn’t establish an absence, that’s actually enough reason to support the rejection. I want to make sure my logic stands up to scrutiny, as it’s important to think through these things clearly. Let’s ensure we’re reinforcing the reasons for a legitimate stance on rejection."
 ]
}

output

{
 "is_pedantic": false,
 "reason": "The rejection is legitimate. The inference requires the factual antecedent that Knapper et al. report no comparative three-laboratory dataset. The previous state does not establish that: “no additional data” does not exclude data presented within the article, and a non-exhaustive description of its calibration workflow does not rule out comparative results elsewhere. This is a plausible substantive evidence-reading error, not merely a demand for extra rigor."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You are the contradiction check on a deterministic grounding. An independent
agent produced an artifact for one proof step (a sympy program, a Lean file,
or a source extraction); the ENGINE then executed or verified it first-hand.
You see the artifact and the engine-witnessed output, and return a verdict
only — never fixes, never advice.

Your verdict gates a hard rejection: `accepted: false` cannot be overturned
downstream, so it must mean a genuine, demonstrated contradiction.

# Decide

Reject (`accepted: false`) only when BOTH hold:
1. The artifact faithfully checks what the step claims — same quantities, same
   relation, computed rather than copied; a checked Lean statement says what
   the step says; verified quotes are about the fact the step relies on.
2. The engine-witnessed output contradicts the step's claimed transformation —
   a different value, a failed relation, a checked Lean statement proving the
   NEGATION of the step's claim, or source text that states something
   incompatible with what the step attributes to it. A proved negation counts
   as faithful for criterion 1: it addresses exactly the step's claim.

Everything else accepts (`accepted: true`), because acceptance is the neutral
outcome — the step still faces its own judge:
- Representation differences are NOT contradictions: 2/4 vs 1/2, sqrt(2)/2 vs
  1/sqrt(2), reordered terms, equivalent phrasing, print formatting.
- An artifact that is not probative — it hardcodes the answer, computes
  something other than the step's claim, states a weaker/stronger theorem, or
  quotes text unrelated to the claim — accepts, with a reason saying the
  grounding was not probative.
- Output you cannot decisively map onto the step's claim accepts.

For extraction groundings, the output lists the fetched source (url + sha256
provenance header) and each quote's alignment: status, char interval, and the
aligned source span. Judge from the SPAN text — that is the source's own
wording, engine-witnessed; the author's quote is only the search key. A
MATCH_FUZZY span whose actual wording states something incompatible with what
the step attributes to the source is exactly the contradiction to reject.

# Reason field
One or two sentences. On rejection, quote the engine-witnessed output verbatim
against the step's claimed value — the repair loop sees only your reason, so
the deterministic evidence must be in it. On acceptance, say what the grounding
established (or why it was not probative). Verdict only: never suggest how to
fix the step.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Step 3 whose grounding is under review:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']
  Justification type: computation
  Justification: The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.

Artifact (produced by an independent grounding agent):
required_quantities = Set(["resolution", "field_curvature", "illumination_uniformity", "stage_repeatability"])

collins_evidence = {
    "independent_laboratories": 1,
    "quantitatively_measured": Set(["resolution"]),
    "certified_targets_for_all_quantities": False,
    "stated_uncertainties_for_comparison": False
}

condition_satisfied = (
    collins_evidence["independent_laboratories"] >= 3
    and required_quantities.issubset(collins_evidence["quantitatively_measured"])
    and collins_evidence["certified_targets_for_all_quantities"]
    and collins_evidence["stated_uncertainties_for_comparison"]
)

print(condition_satisfied)


Engine-witnessed output:
False

output

{
 "accepted": true,
 "reason": "The computed conjunction is false under the encoded evidence, which agrees with the step’s claim that Collins et al. do not satisfy the three-laboratory, four-quantity condition."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You decide whether a judge's legitimate rejection can be resolved
by invoking a single standard, domain-level convention. This is
the LAST chance for a proof step; if you lift, the step becomes
accepted-under-assumption and its convention is recorded in the
proof's list of added assumptions. If you don't lift, the step
stays rejected and the proof is not verified.

Be VERY conservative. A convention qualifies ONLY if ALL of:

1. ASYMMETRIC DEFAULT: the opposite of this assumption would
   have to be explicitly stated by the author if they meant
   it. Practitioners invoke this default automatically when
   the problem is silent about it. If BOTH the assumption and
   its opposite are equally plausible when the problem omits
   the detail, NEITHER is a convention — the problem is
   genuinely ambiguous between them, and you must not lift.

2. Verifiable source: the assumption is either explicitly
   stated as default in a published reference, or pervasively
   used without statement in published references for this
   problem class. Provide a URL or textbook+section. Use web
   search to verify.

3. Once added as a premise, fully justifies the rejected step
   — the rejection reason must disappear when the convention
   is added.

Do NOT lift: specific numeric values, instantiated parameters,
interpretations where multiple equally-plausible defaults
exist, or convenience simplifications that the author might
reasonably not have intended.

Required output:
  can_lift: boolean — true only if all three criteria met
  convention: the convention stated as an explicit added premise
  source: published reference (URL or textbook+section)
  reasoning: brief explanation of why all three criteria are met,
             or why they aren't

When in doubt, can_lift = false. The benchmark's trustworthiness
depends on you being strict. Treat this the same way you'd treat
a decision to publish: would a skeptical reader of a paper accept
this convention as canonical?

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 1 being evaluated:
  Previous state: ['ANSWER']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  Justification type: problem_given
  Justification: This is the conjunctive evidentiary requirement stated in the question.

Judge's rejection reason:
1. The problem does not state that the measurements must be published; “published” is an added evidentiary premise.
2. The problem says “across three independent labs,” not “at least three independent laboratories.” Treating this as a minimum of three is an interpretation rather than a directly stated value.

Pedantry already confirmed this rejection is legitimate:
The rejection is legitimate because Step 1 adds a substantive requirement that the measurements be published. The question asks whether the measurements agree, not merely whether published evidence demonstrates agreement; unpublished or otherwise available three-lab results could make the answer positive. Interpreting “across three” as “at least three” is harmless, but the added publication premise could lead to an incorrect negative answer.

Is there a single standard, citable, domain-wide convention that — if added as an explicit premise — would fully justify this step and resolve the judge's objection?

reasoning

{
 "summary": [
  "**Searching for ISO definitions**\n\nI need to find the exact JSON schema for the user’s request, so a web search seems essential. I'm questioning whether a convention can support a publication premise — it seems clear that it cannot. I might need to cite a source, maybe from convention, but if it’s false, no source has verified that. I should look into ISO’s metrology and proficiency testing definitions, as they might have confidential results. I'll search for official definitions that can guide me."
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "site:iso.org ISO 17043 proficiency testing confidentiality results participants publication",
   "site:eurachem.org interlaboratory comparison published results definition",
   "site:bipm.org interlaboratory comparison definition publication results"
  ],
  "query": "site:iso.org ISO 17043 proficiency testing confidentiality results participants publication"
 }
}

output

{
 "can_lift": false,
 "convention": "None. Interlaboratory agreement is not conventionally restricted to measurements that have been published.",
 "source": "Eurachem, “Fundamental Terms in Proficiency Testing,” definition of interlaboratory comparison: https://www.eurachem.org/images/stories/wgs/PT/docs/fundamental_terms_in_pt_discussionpaperfinal.pdf",
 "reasoning": "The cited metrology definition requires measurements by multiple laboratories under predetermined conditions but does not require public or peer-reviewed reporting. Unpublished laboratory results could therefore answer the original factual question. Although “across three” can harmlessly include three or more laboratories, no asymmetric, domain-wide convention supplies the added publication premise, so a single convention cannot fully cure the rejection."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You extract the exact source text a proof step rests on — FROM THE PAGE TEXT
PROVIDED IN THE PROMPT. The engine fetched that text itself and will align
every quote you return against exactly those bytes, token-by-token (bounded
tolerance for whitespace, casing, and typographic punctuation — never
paraphrase, never quote from memory). A separate analyst then judges whether
the engine-verified spans actually license the step.

# Goal
From the provided page text, put in `quotes` the substring(s) that state the
result the step invokes, copied from the page text as-is.

`claim_mapping`: one or two sentences on how the quotes license this step's
BEFORE -> AFTER transformation — including what they do NOT cover, if the
justification claims more than the source states.

# Success criteria
- Every quote is copied from the provided text, not composed or recalled.
- Quotes are the minimal spans that state the relied-on fact — not whole
  paragraphs, not fragments too short to assert anything. Prefer plain-prose
  statements; avoid regions mangled by leftover markup.
- If a multi-part theorem is involved, quote enough that cherry-picking
  would be visible.

# If the page does not state it
If the provided text does not contain what the step attributes to the
source, return your best honest extraction anyway (the nearest relevant
passage) and say in `claim_mapping` that it does not support the claim — the
analyst, not you, decides whether that is a contradiction.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Step 2 whose citation needs quoting:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']
  Justification: Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))

Source page (fetched by the engine from https://pmc.ncbi.nlm.nih.gov/articles/PMC7249832/):
---



    
    
        
    
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Biomed Opt Express
. 2020 Apr 8;11(5):2447–2460. doi: 10.1364/BOE.385729





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Robotic microscopy for everyone: the OpenFlexure microscope


Joel T Collins


Joel T Collins



1Centre for Photonics and Photonic Materials, Department of Physics, University of Bath, UK


Find articles by Joel T Collins




1, Joe Knapper


Joe Knapper



1Centre for Photonics and Photonic Materials, Department of Physics, University of Bath, UK


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1, Julian Stirling


Julian Stirling



1Centre for Photonics and Photonic Materials, Department of Physics, University of Bath, UK


Find articles by Julian Stirling




1, Joram Mduda


Joram Mduda



2Ifakara Health Institute, Ifakara, Tanzania


Find articles by Joram Mduda




2, Catherine Mkindi


Catherine Mkindi



2Ifakara Health Institute, Ifakara, Tanzania


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2, Valeriana Mayagaya


Valeriana Mayagaya



2Ifakara Health Institute, Ifakara, Tanzania


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2, Grace A Mwakajinga


Grace A Mwakajinga



3STICLab, Dar Es Salaam, Tanzania


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3, Paul T Nyakyi


Paul T Nyakyi



3STICLab, Dar Es Salaam, Tanzania


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3, Valerian L Sanga


Valerian L Sanga



3STICLab, Dar Es Salaam, Tanzania


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3, Dave Carbery


Dave Carbery



4Department of Chemistry, University of Bath, UK


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4, Leah White


Leah White



4Department of Chemistry, University of Bath, UK


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4, Sara Dale


Sara Dale



5Centre for Nanoscience and Nanotechnology, Department of Physics, University of Bath, UK


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5, Zhen Jieh Lim


Zhen Jieh Lim



5Centre for Nanoscience and Nanotechnology, Department of Physics, University of Bath, UK


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5, Jeremy J Baumberg


Jeremy J Baumberg



6Nanophotonics Centre, Cavendish Laboratory, University of Cambridge, UK


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6, Pietro Cicuta


Pietro Cicuta



7Cavendish Laboratory, University of Cambridge, UK


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7, Samuel McDermott


Samuel McDermott



7Cavendish Laboratory, University of Cambridge, UK


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7, Boyko Vodenicharski


Boyko Vodenicharski



7Cavendish Laboratory, University of Cambridge, UK


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7, Richard Bowman


Richard Bowman



1Centre for Photonics and Photonic Materials, Department of Physics, University of Bath, UK


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1,*





Author information


Article notes


Copyright and License information









1Centre for Photonics and Photonic Materials, Department of Physics, University of Bath, UK



2Ifakara Health Institute, Ifakara, Tanzania



3STICLab, Dar Es Salaam, Tanzania



4Department of Chemistry, University of Bath, UK



5Centre for Nanoscience and Nanotechnology, Department of Physics, University of Bath, UK



6Nanophotonics Centre, Cavendish Laboratory, University of Cambridge, UK



7Cavendish Laboratory, University of Cambridge, UK




*
Email: r.w.bowman@bath.ac.uk










Received 2019 Dec 12; Revised 2020 Mar 6; Accepted 2020 Mar 9; Collection date 2020 May 1.







Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.


Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.


PMC Copyright notice






PMCID: PMC7249832  PMID: 32499936









Abstract


Optical microscopes are an essential tool for both the detection of disease in clinics, and for scientific analysis. However, in much of the world access to high-performance microscopy is limited by both the upfront cost and maintenance cost of the equipment. Here we present an open-source, 3D-printed, and fully-automated laboratory microscope, with motorised sample positioning and focus control. The microscope is highly customisable, with a number of options readily available including trans- and epi- illumination, polarisation contrast imaging, and epi-florescence imaging. The OpenFlexure microscope has been designed to enable low-volume manufacturing and maintenance by local personnel, vastly increasing accessibility. We have produced over 100 microscopes in Tanzania and Kenya for educational, scientific, and clinical applications, demonstrating that local manufacturing can be a viable alternative to international supply chains that can often be costly, slow, and unreliable.



1. Introduction


For centuries optical microscopy has been the foundation of scientific imaging and analysis in many aspects of medicine, life, and physical sciences [1]. Commercially available high-end microscopes can provide precise motorised high-resolution imaging capabilities, however these are often prohibitively expensive. This is compounded in the developing world where unreliable supply chains inflate prices, and slow acquisition [2]. Maintaining equipment adds further burden as devices have often not been designed for these operating environments [3], and neither manufacturers representatives nor spare parts are available locally, leading to much of the laboratory equipment in resource-poor countries being out-of-service [4].


Open-source hardware is poised to revolutionise the distribution of scientific instrumentation, impacting research, local manufacturing, and education [5,6]. Open science hardware designs are already in use for both research and education across a wide range of disciplines [7–11]. Within research laboratories in particular, 3D printers have become an increasingly common item of equipment. This has led a number of open science hardware projects to use 3D printing as an accessible platform for locally prototyping and manufacturing laboratory-grade devices [10–12].


Here we present the OpenFlexure Microscope (OFM), a 3D-printed, laboratory-grade automated microscope. The OFM aims to make automated microscopy accessible both to projects with a modest budget in established labs, and to developing nations aiming to adopt more advanced scientific research technologies. Unlike other low-cost open-source microscopes the OFM has a strong focus on providing precise 3D motion for focus and sample positioning, built around a well-characterised flexure mechanism [13]. This mechanism provides 3-axis positioning with step sizes as low as 50 nm in the z axis, and 70 nm in x and y. The range of mechanical motion is smaller than traditional mechanical stages, with 12×12×4 mm travel, and due to the primarily plastic construction, our design has a limited load capacity unsuitable for very large or heavy samples. However, both the range of motion, and load capacity, are ample for most microscopy applications. The microscope is both compact, fitting within a 15cm×15cm×20cm volume, and lightweight at ≈ 500 g in its highest resolution, fully automated configuration. The microscope is designed to be highly modular, and while the positioning mechanism is standard across all configurations, illumination, optics, and imaging can be completely customized. A range of included interchangeable optics modules enable different imaging modalities (Section 2.1) allowing different cameras and imaging lenses to be used for applications from blood smear parasitology to school teaching.


The OFM has now been trialled in a range of applications, and reproduced by a number of groups around the world. The design (Fig. 1) has been refined to reduce assembly time, ease component sourcing, and maximise reliability. These ongoing optimisations are key to a sustainable and useful open hardware project that is trusted for critical applications. Version 6.0 of the OpenFlexure Microscope represents a well tested microscopy platform, enabling the rapid prototyping of new instrumentation, and replication of high quality research tools, even in resource-poor settings.


Fig. 1.





Open in a new tab


Overview of the OpenFlexure Microscope design, in transmission bright-field configuration. The condenser mount houses an illumination LED and a plastic condenser lens, while the optics module sits below the stage and houses an objective lens, tube lens, and camera. The entire optics module is attached to the z-actuator, providing variable focus. Both the optics module and x-y stage are controlled by actuator gears at the back of the microscope, optionally driven by stepper motors. A detachable electronics housing stores optional electronic parts, such as motor controllers and a Raspberry Pi, for automation.



2. Imaging capabilities


The OpenFlexure Microscope uses an interchangeable optics module to easily change between imaging modes. Most of the optics modules use standard RMS objectives to yield high-quality images expected from a laboratory microscope, and an option is available to use an inverted, spatially offset webcam lens to provide magnification at a low-cost for educational use. The estimated parts costs for various configurations of the microscope are provided in Appendix A.1.


We employ an 8MP CMOS sensor (Raspberry Pi camera V2) to provide digital imaging capabilities. The front lens of the camera is easily unscrewed and removed, allowing the optics module to properly function while still providing high-quality imaging. Many low-cost microscopy projects make use of smartphone cameras for imaging [14–16], however as these retain the smartphone lens as part of the optical path they usually require additional costly optical components. In contrast, by using a well characterized, widely available sensor (Sony IMX219) [17], the OFM is able to reliably reproduce the reported imaging quality at minimal cost. Furthermore, a permanent, low-cost imaging sensor makes long-running automated experiments significantly more practical, as discussed in section 2.3. A comprehensive radiometric characterization of the IMX219 sensor has quantified the shot, read, and fixed-pattern noise of the sensor, its spectral response, and its stability, demonstrating the Raspberry Pi camera’s suitability for scientific imaging [18].


The high-quality optics module makes use of achromatic objectives and an achromatic tube lens to minimize chromatic aberrations. While narrow-band illumination sources would help further minimize chromatic aberrations, full-color white light imaging is typically required for our applications such as blood parasite imaging (section 2.1.1) and graphene flake imaging (section 2.1.2). Nevertheless, by introducing achromatic optics, the dominant chromatic effect becomes the chief ray angle color mixing, which can be largely mitigated with software calibration [19].


OFM optics modules are available for bright-field (with both trans- and epi- illumination) imaging, polarisation contrast imaging, and epifluorescence imaging. Additionally, both finite and infinite conjugate objectives can be used by varying the position of the tube lens. Figure 2 provides schematics of trans- (a.) and epi- (b.) illumination configurations. Fluorescence imaging is realised by inserting a dichroic filter in position F1, and a long-pass filter in position F2 of the removable filter cube. The cube is connected to a reflection illuminator (L3, LED2) with suitable LED illumination. Bright-field epi- imaging is achieved by removing filter F2, and using a standard beamsplitter in position F1. Polarisation contrast imaging requires transmission illumination (Fig. 2(a)), with a linear polariser in filter cube position F2.


Fig. 2.





Open in a new tab


Cross-section schematics of trans- (a.) and epi- (b.) illumination configurations. LED1 provides transmission illumination, with a condenser lens L1. LED2 and lens L3 provide epi-illumination, connected to a removable filter cube housing two filters, F1 at 45° and F2. These filters can be removed or replaced by beamsplitters or polarizers to enable bright-field, fluorescence, or polarization-contrast epi-illuminated imaging. In both configurations, a standard RMS objective O1 and tube lens L2 image the sample onto the camera sensor CAM.

Images in this section are obtained with an RMS objective (100×, 1.25NA oil immersion, or 40×, 0.65NA dry), an f=50 mm tube lens (ThorLabs AC127-050-A), and an 8MP CMOS sensor (Raspberry Pi camera V2) (Fig. 3(a)).


Fig. 3.





Open in a new tab


Schematics (left) and images (right) of four different imaging modalities possible using the OFM. a. Trans-illumination bright-field imaging of a Giemsa-stained thin blood smear, obtained with a 100×, 1.25NA oil immersion objective. The inset shows a magnified section of the image, highlighting a ring-form trophozoite of Plasmodium falciparum. b. Epi-illumination bright-field imaging of a group of thin graphene flakes, obtained with a 40×, 0.65NA dry objective. The inset shows a magnified section of the image, highlighting a resolvable tri-layer graphene flake (contrast has been digitally enhanced for clarity by increasing brightness and gamma). c. Polarisation-contrast trans-illumination image of 5CB liquid crystal droplets. A bright-field image is shown below for comparison. Both images were obtained with a 40×, 0.65NA dry objective, and depict the same region of the sample. Arrows on the polarisers denote the transmission axis. d. Fluorescence images of unstained Lily of the Valley (convallaria majalis) rhizome, at two different wavelengths. The excitation wavelength (“Ex.”), and minimum emission wavelength imaged (“Em.”) are shown above the respective panels. Both images were obtained with a 40×, 0.65NA dry objective, and depict the same region of the sample. Both the colour of illumination LED, and the filters in the filter cube, will change depending on the application.


2.1. Imaging modes



2.1.1. Bright-field trans-illumination


Bright-field trans-illumination is the “standard” imaging mode for the OFM. White light illumination, provided by an LED, is focused onto the sample using an f=5 mm PMMA condenser lens. LED illumination is diffused by sanding the LED case, preventing the condenser from imaging the chip onto a sample. Figure 3(a) shows an image of a Giemsa-stained blood smear, obtained at the Ifakara Health Institute for the purpose of malaria diagnosis. The image is obtained with a 100×, 1.25NA oil immersion objective and a 16.25 ms acquisition time. The microscope was vibrationally isolated with a layer of foam below the device. In this configuration, individual red blood cells, with dimensions on the order of microns, are clearly resolved. A ring-form trophozoite of Plasmodium falciparum within a red blood cell is highlighted in the figure inset (contrast has been digitally enhanced for clarity by increasing brightness and gamma). Despite being only 1 µm to 2 µm across, the morphology of these ring-form parasites is also clearly resolved by the OFM.


Image quality is in line with expectations for manual microscopes currently used for malaria diagnosis. However, digital images make it possible to re-examine a slide without physically preserving and transporting it. This improves record-keeping, quality control, and training of both new and experienced technicians. Automatic acquisition of images (Section 2.3) goes further, improving throughput of samples and paving the way for automated image processing to assist diagnostic technicians.



2.1.2. Bright-field epi-illumination


Reflection (epi-) bright-field imaging is enabled by inserting a 50/50 beam splitter at 45° within a printed filter cube between the tube lens and the sensor. Illumination is provided by a collimated diffused LED reflected through the objective by the beamsplitter (Fig. 2(b)). Light reflected from the sample is partially transmitted through the beam splitter and onto the sensor, enabling imaging of opaque samples.


Figure 3(b) shows graphene flakes on a 300 nm SiO2/Si substrate, illuminated with a white LED, and imaged using a 40×, 0.65NA dry objective with a 9 ms acquisition time. This provides enough resolving power to image typical graphene flakes, while simplifying use by removing the need for immersion oil. Illumination is provided by a Nichia NSPL500DS white LED, with ≈20 µW power at the sample plane. Graphene flakes, produced via mechanical exfoliation, are widely used to study novel electrical and mechanical properties of 2D materials [20]. Thin graphene flakes, with random positions and thicknesses across the substrate, are commonly identified by manual optical microscopy. Subtle variations in the colour and intensity of transmitted light (≈2.3% absorption per layer [20,21]) can be used to estimate their thickness. This method of identifying flakes is both time consuming and subjective when performed manually, but can be automated with the OFM. Raman spectroscopy measurements have confirmed that the flake highlighted in Fig. 3(b) is tri-layer graphene. Unlike other methods of identifying flakes (AFM, Raman spectroscopy, etc.), this searching method is high speed and low-cost, and the graphene is not damaged. By optimising illumination for the detection of graphene flakes [22,23], and improving image processing [20], we estimate the OFM can resolve even monolayer graphene, and we have also imaged the transition metal dichalcogenide molybdenum disulphide with similar success.



2.1.3. Polarisation-contrast imaging


Many microscopic structures important to biology and biochemistry benefit from polarisation-contrast imaging [24–26]. Anisotropic or chiral structures can rotate the polarisation vector of light propagating through them. The OFM can be used for polarisation-contrast imaging by placing a one linear polariser between the illumination and the sample, and an orthogonal polariser between the tube lens and the sensor. Light that passes through the sample unchanged is extinguished, thus only chiral or anisotropic regions of the sample are imaged. Figure 3(c) shows an image of 4-Cyano-4′-pentylbiphenyl (5CB) liquid crystal droplets, obtained in polarisation-contrast mode with a 40× objective (the same as used previously) and 1.3 ms acquisition times. Illumination is provided by a Nichia NSPL500DS white LED, with ≈250 µW power at the sample plane. Edmund Optics Visible Linear Polarizing Laminated Film (Family ID 1912) was used to both polarize the illumination and analyze the image. The sample was prepared by adding a drop of 5CB liquid crystal to the slide, followed by acetone to form a film. The film is imaged without a cover slip, requiring a dry objective. The droplets can be seen clearly in the bright-field transmission illumination image, and the liquid crystal orientation structure can be seen in the cross-polarised image. The isotropic background is extinguished, appearing dark. Within the droplets, dark regions appear when the 5CB is aligned parallel or perpendicular to the illumination polarisation, and bright regions appear as the crystal orientation deviates from this.



2.1.4. Fluorescence imaging


Fluorescence microscopy is one of the most important and powerful methods for investigating a range of biological processes. By illuminating a fluorescent sample with suitable excitation-wavelength light, emitted light with a Stokes shift in wavelength can be observed. The OFM can perform low-cost fluorescence microscopy by inserting a dichroic beam splitter and optical filters within a printed filter cube between the tube lens and the sensor, and illuminating with an LED of the desired excitation wavelength (Fig. 2(b)).


Figure 3(d) shows fluorescence images of unstained Lily of the Valley (convallaria majalis) rhizome taken on the OFM. The same 40× dry objective is used to provide a suitable magnification for the convallaria majalis sample. Stray light from external sources at the emission wavelength is minimized by covering the top region of the microscope in a compact opaque box. Two excitation wavelengths (480 nm and 525 nm, with corresponding fluorescence filters as shown in the figure) were used.


Illumination at 480 nm is provided by a Cree C503B-BCS LED, with ≈40 µW at the sample plane. Fluorescence at >510 nm (green) is imaged using a long-pass dichroic (Comar Instruments 550 IY 50) and emission filter (Comar Instruments 510 IY 125), with a 33 ms acquisition time. 525 nm illumination is provided by a Broadcom HLMP-CM2H-130DD LED. Fluorescence at >590 nm (red) is imaged using a long-pass dichroic (Comar Instruments 635 IY 125) and emission filter (Comar Instruments 590 GY 50), with a 600 ms acquisition time.


The inclusion of rubber feet enables a level of vibration damping suitable for acquisition times of the order of hundreds of milliseconds, and can be further improved by situating the microscope in a suitably isolated location, for example on an optical table, and away from desks used for active work. On short time scales (seconds), Allan deviation on the ord
---

output

{
 "quotes": [
  "The high-quality optics module makes use of achromatic objectives and an achromatic tube lens to minimize chromatic aberrations. While narrow-band illumination sources would help further minimize chromatic aberrations, full-color white light imaging is typically required for our applications such as blood parasite imaging (section 2.1.1) and graphene flake imaging (section 2.1.2). Nevertheless, by introducing achromatic optics, the dominant chromatic effect becomes the chief ray angle color mixing, which can be largely mitigated with software calibration [19].",
  "In this configuration, individual red blood cells, with dimensions on the order of microns, are clearly resolved. A ring-form trophozoite of Plasmodium falciparum within a red blood cell is highlighted in the figure inset (contrast has been digitally enhanced for clarity by increasing brightness and gamma). Despite being only 1 µm to 2 µm across, the morphology of these ring-form parasites is also clearly resolved by the OFM."
 ],
 "claim_mapping": "These passages provide only nearby statements about optical aberration mitigation and qualitative resolving performance. The supplied page text ends before section 2.2 and does not state the claimed USAF-target method, 480 nm FWHM, central-50% result, field-curvature edge degradation, lens-shading-table correction, uncertainty budgets, or absence of a three-laboratory comparison."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You are the contradiction check on a deterministic grounding. An independent
agent produced an artifact for one proof step (a sympy program, a Lean file,
or a source extraction); the ENGINE then executed or verified it first-hand.
You see the artifact and the engine-witnessed output, and return a verdict
only — never fixes, never advice.

Your verdict gates a hard rejection: `accepted: false` cannot be overturned
downstream, so it must mean a genuine, demonstrated contradiction.

# Decide

Reject (`accepted: false`) only when BOTH hold:
1. The artifact faithfully checks what the step claims — same quantities, same
   relation, computed rather than copied; a checked Lean statement says what
   the step says; verified quotes are about the fact the step relies on.
2. The engine-witnessed output contradicts the step's claimed transformation —
   a different value, a failed relation, a checked Lean statement proving the
   NEGATION of the step's claim, or source text that states something
   incompatible with what the step attributes to it. A proved negation counts
   as faithful for criterion 1: it addresses exactly the step's claim.

Everything else accepts (`accepted: true`), because acceptance is the neutral
outcome — the step still faces its own judge:
- Representation differences are NOT contradictions: 2/4 vs 1/2, sqrt(2)/2 vs
  1/sqrt(2), reordered terms, equivalent phrasing, print formatting.
- An artifact that is not probative — it hardcodes the answer, computes
  something other than the step's claim, states a weaker/stronger theorem, or
  quotes text unrelated to the claim — accepts, with a reason saying the
  grounding was not probative.
- Output you cannot decisively map onto the step's claim accepts.

For extraction groundings, the output lists the fetched source (url + sha256
provenance header) and each quote's alignment: status, char interval, and the
aligned source span. Judge from the SPAN text — that is the source's own
wording, engine-witnessed; the author's quote is only the search key. A
MATCH_FUZZY span whose actual wording states something incompatible with what
the step attributes to the source is exactly the contradiction to reject.

# Reason field
One or two sentences. On rejection, quote the engine-witnessed output verbatim
against the step's claimed value — the repair loop sees only your reason, so
the deterministic evidence must be in it. On acceptance, say what the grounding
established (or why it was not probative). Verdict only: never suggest how to
fix the step.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Step 8 whose grounding is under review:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  New state: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']
  Justification type: computation
  Justification: Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Artifact (produced by an independent grounding agent):
# Propositions:
# E: the necessary evidentiary condition is met
# D: the claimed interlaboratory agreement is demonstrated
# X: the laboratories actually disagree
#
# Previous state gives not E. The justification gives D => E.

models = []
for E in [False, True]:
    for D in [False, True]:
        for X in [False, True]:
            if ((not D) or E) and (not E):
                models.append((E, D, X))

def forced_value(index):
    values = Set(model[index] for model in models)
    if values == Set([True]):
        return True
    if values == Set([False]):
        return False
    return "undetermined"

print("agreement demonstrated:", forced_value(1))
print("laboratories disagree:", forced_value(2))

Engine-witnessed output:
agreement demonstrated: False
laboratories disagree: undetermined

output

{
 "accepted": true,
 "reason": "The grounding establishes that if demonstration requires the evidentiary condition and that condition is absent, agreement is not demonstrated, while actual disagreement remains undetermined. This matches the step’s claimed transformation."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You are a pedantry filter for a verified-reasoning pipeline. A judge
has rejected a step in a proof. Your job is to decide whether the
rejection is LEGITIMATE (the proof is actually wrong) or PEDANTIC
(the proof is correct, the judge demanded more rigor than necessary
for this kind of problem).

If ANY numbered issue in the rejection looks like it points to an
error an LLM could plausibly make that would lead to a legitimately
incorrect answer, mark it as is_pedantic=false. A step is pedantic
ONLY if EVERY issue listed is pedantic. The whole point is to catch
real errors; don't downgrade something that could be a hallucination,
arithmetic mistake, fabricated citation, or wrong fact.

Use web search if you need to verify whether a citation or factual
claim is real before deciding.

Be CONSERVATIVE — when in doubt, mark as legitimate (is_pedantic=
false). The system needs to catch real errors more than it needs
to push borderline cases through.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 6 being evaluated:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  Justification type: citation
  Justification: Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))

A judge rejected this step with the following reason:
1. The catalogue is not represented as exhaustive. Its “Citing publications” section explicitly asks users to notify the project so publications can be added, so absence from this list cannot establish absence of a qualifying peer-reviewed study. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
2. “Current through work listed for 2026” is unsupported and misleading. The page lists two 2026 papers only under “Citing publications,” while the project’s own “Publications and conferences” list ends in 2024; inclusion of some 2026 citations does not demonstrate comprehensive coverage through August 31, 2026. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
3. The catalogue supplies mainly bibliographic entries and titles. It does not document that every listed paper was inspected for measurements from three laboratories, all four quantities, certified targets, and uncertainty budgets. Therefore it cannot by itself justify the detailed content-based negative claim.
4. The page combines journal articles, conference papers, presentations, preprints, and citing publications, including an F1000Research item whose displayed peer-review status includes one approval and one non-approval. Thus the citation does not provide a clean, defined catalogue of exclusively peer-reviewed entries matching the claim’s characterization. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))

Is this rejection legitimate (the proof is actually wrong) or pedantic (the proof is correct, the judge is being too strict)?

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://openflexure.gitlab.io/about/publications"
 }
}

output

{
 "is_pedantic": false,
 "reason": "The rejection is legitimate. The cited page expressly presents a user-notified collection rather than an exhaustive bibliography, mixes project outputs with citing publications and nonuniform publication types/statuses, and does not show that every listed work was inspected for the detailed four-quantity, three-laboratory uncertainty comparison. Its two 2026 citing entries also do not support claiming comprehensive coverage through August 31, 2026. Therefore the catalogue alone cannot establish the asserted absence of any qualifying peer-reviewed study."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You are the contradiction check on a deterministic grounding. An independent
agent produced an artifact for one proof step (a sympy program, a Lean file,
or a source extraction); the ENGINE then executed or verified it first-hand.
You see the artifact and the engine-witnessed output, and return a verdict
only — never fixes, never advice.

Your verdict gates a hard rejection: `accepted: false` cannot be overturned
downstream, so it must mean a genuine, demonstrated contradiction.

# Decide

Reject (`accepted: false`) only when BOTH hold:
1. The artifact faithfully checks what the step claims — same quantities, same
   relation, computed rather than copied; a checked Lean statement says what
   the step says; verified quotes are about the fact the step relies on.
2. The engine-witnessed output contradicts the step's claimed transformation —
   a different value, a failed relation, a checked Lean statement proving the
   NEGATION of the step's claim, or source text that states something
   incompatible with what the step attributes to it. A proved negation counts
   as faithful for criterion 1: it addresses exactly the step's claim.

Everything else accepts (`accepted: true`), because acceptance is the neutral
outcome — the step still faces its own judge:
- Representation differences are NOT contradictions: 2/4 vs 1/2, sqrt(2)/2 vs
  1/sqrt(2), reordered terms, equivalent phrasing, print formatting.
- An artifact that is not probative — it hardcodes the answer, computes
  something other than the step's claim, states a weaker/stronger theorem, or
  quotes text unrelated to the claim — accepts, with a reason saying the
  grounding was not probative.
- Output you cannot decisively map onto the step's claim accepts.

For extraction groundings, the output lists the fetched source (url + sha256
provenance header) and each quote's alignment: status, char interval, and the
aligned source span. Judge from the SPAN text — that is the source's own
wording, engine-witnessed; the author's quote is only the search key. A
MATCH_FUZZY span whose actual wording states something incompatible with what
the step attributes to the source is exactly the contradiction to reject.

# Reason field
One or two sentences. On rejection, quote the engine-witnessed output verbatim
against the step's claimed value — the repair loop sees only your reason, so
the deterministic evidence must be in it. On acceptance, say what the grounding
established (or why it was not probative). Verdict only: never suggest how to
fix the step.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Step 6 whose grounding is under review:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  Justification type: citation
  Justification: Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))

Artifact (produced by an independent grounding agent):
The page characterizes itself as a collection of OpenFlexure scholarly outputs, lists its project publications, and separately includes citing work dated 2026; inspection of the displayed project-publication titles reveals no three-laboratory study jointly covering the four named quantities. The page does not explicitly state that no such study exists, that the catalogue is complete or current through 2026, or that the listed papers lack the specified measurements and uncertainty budgets, so those parts are inferences from the catalogue rather than source-stated facts.
quote 1 (author): 'A collection of journal articles, conference papers, and other scholarly outputs produced through the OpenFlexure project and its international research collaborations.'
quote 2 (author): 'Developing the OpenFlexure Microscope towards medical use: technical and social challenges of developing globally accessible hardware for healthcare \n     \n    \n      Philosophical Transactions of the Royal Society A  ·  2024\n    \n     \n  \n\n  \n  \n\n    \n     Utility of a low-cost 3-D printed microscope for evaluating esophageal biopsies \n     \n    \n      Annals of 3D Printed Medicine  ·  2024\n    \n     \n  \n\n  \n  \n\n    \n     Controlling and scripting laboratory hardware with open-source, intuitive interfaces: OpenFlexure Voice Control and OpenFlexure Blockly \n     \n    \n      Royal Society Open Science  ·  2023\n    \n     \n    \n       [\n        arXiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     Multi-modal microscopy imaging with the OpenFlexure Delta Stage \n     \n    \n      Optics Express  ·  2022\n    \n     \n    \n       [\n        arXiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     Simplifying the OpenFlexure Microscope software with the web of things \n     \n    \n      Royal Society Open Science  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     Fast, high precision autofocus on a motorised microscope: automating blood sample imaging on the OpenFlexure Microscope \n     \n    \n      Journal of Microscopy  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     HardOps: Utilising the software development toolchain for hardware design \n     \n    \n      International Journal of Computer Integrated Manufacturing  ·  2021\n    \n     \n    \n       [\n        TechRxiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     An Open‐Source Modular Framework for Automated Pipetting and Imaging Applications \n     \n    \n      Advanced Biology  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     Transitioning from Academic Innovation to Viable Humanitarian Technology: The Next Steps for the OpenFlexure Project \n     \n    \n      IST-Africa conference  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     Low-cost, multimodal bioimaging with the OpenFlexure Delta Stage Microscope \n     \n    \n      RMS Frontiers in Bioimaging  ·  2020\n    \n     \n  \n\n  \n  \n\n    \n     The OpenFlexure Project. The technical challenges of Co-Developing a microscope in the UK and Tanzania \n     \n    \n      IEEE Global Humanitarian Technology Conference (GHTC)  ·  2020\n    \n     \n    \n       [\n        AfricaArXiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     Robotic microscopy for everyone: the OpenFlexure Microscope \n     \n    \n      Biomedical Optics Express  ·  2020\n    \n     \n    \n       [\n        bioRxiv ]   🏆\n       Best paper prize \n      \n    \n    \n  \n\n  \n  \n\n    \n     The OpenFlexure Block Stage: sub-100 nm fibre alignment with a monolithic plastic flexure stage \n     \n    \n      Optics Express  ·  2020\n    \n     \n  \n\n  \n  \n\n    \n     Flat-Field and Colour Correction for the Raspberry Pi Camera Module \n     \n    \n      Journal of Open Hardware  ·  2020\n    \n     \n  \n\n  \n  \n\n    \n     A one-piece 3D printed flexure translation stage for open-source microscopy \n     \n    \n      Review of Scientific Instruments  ·  2016'
quote 3 (author): 'Srivastava, J., Curd, M. E., Yao, Y., Holroyd, N. J. H., Shanthraj, P., Singh, S. B., Mandal, S., Prangnell, P. B. and Burnett, T. L. Effect of quench- and age-induced grain boundary η-phase precipitates on hydrogen environmentally induced cracking (H-EIC) behaviour of AA7085 alloy in humid air. Journal of Materials Science. (2026)'

Engine-witnessed output:
source: https://openflexure.gitlab.io/about/publications sha256=91b1e46221ad3bb7e18751125ff36e54bd4aaaebe995900e667fe49dd0451a81 19014 chars
quote 1: MATCH_EXACT [8496..8664] 'A collection of journal articles, conference papers, and other scholarly outputs produced through the OpenFlexure project and its international research collaborations.'
quote 2: MATCH_EXACT [9195..12124] 'Developing the OpenFlexure Microscope towards medical use: technical and social challenges of developing globally accessible hardware for healthcare \n     \n    \n      Philosophical Transactions of the Royal Society A  ·  2024\n    \n     \n  \n\n  \n  \n\n    \n     Utility of a low-cost 3-D printed microscope for evaluating esophageal biopsies \n     \n    \n      Annals of 3D Printed Medicine  ·  2024\n    \n     \n  \n\n  \n  \n\n    \n     Controlling and scripting laboratory hardware with open-source, intuitive interfaces: OpenFlexure Voice Control and OpenFlexure Blockly \n     \n    \n      Royal Society Open Science  ·  2023\n    \n     \n    \n       [\n        arXiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     Multi-modal microscopy imaging with the OpenFlexure Delta Stage \n     \n    \n      Optics Express  ·  2022\n    \n     \n    \n       [\n        arXiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     Simplifying the OpenFlexure Microscope software with the web of things \n     \n    \n      Royal Society Open Science  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     Fast, high precision autofocus on a motorised microscope: automating blood sample imaging on the OpenFlexure Microscope \n     \n    \n      Journal of Microscopy  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     HardOps: Utilising the software development toolchain for hardware design \n     \n    \n      International Journal of Computer Integrated Manufacturing  ·  2021\n    \n     \n    \n       [\n        TechRxiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     An Open‐Source Modular Framework for Automated Pipetting and Imaging Applications \n     \n    \n      Advanced Biology  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     Transitioning from Academic Innovation to Viable Humanitarian Technology: The Next Steps for the OpenFlexure Project \n     \n    \n      IST-Africa conference  ·  2021\n    \n     \n  \n\n  \n  \n\n    \n     Low-cost, multimodal bioimaging with the OpenFlexure Delta Stage Microscope \n     \n    \n      RMS Frontiers in Bioimaging  ·  2020\n    \n     \n  \n\n  \n  \n\n    \n     The OpenFlexure Project. The technical challenges of Co-Developing a microscope in the UK and Tanzania \n     \n    \n      IEEE Global Humanitarian Technology Conference (GHTC)  ·  2020\n    \n     \n    \n       [\n        AfricaArXiv ]  \n    \n    \n  \n\n  \n  \n\n    \n     Robotic microscopy for everyone: the OpenFlexure Microscope \n     \n    \n      Biomedical Optics Express  ·  2020\n    \n     \n    \n       [\n        bioRxiv ]   🏆\n       Best paper prize \n      \n    \n    \n  \n\n  \n  \n\n    \n     The OpenFlexure Block Stage: sub-100 nm fibre alignment with a monolithic plastic flexure stage \n     \n    \n      Optics Express  ·  2020\n    \n     \n  \n\n  \n  \n\n    \n     Flat-Field and Colour Correction for the Raspberry Pi Camera Module \n     \n    \n      Journal of Open Hardware  ·  2020\n    \n     \n  \n\n  \n  \n\n    \n     A one-piece 3D printed flexure translation stage for open-source microscopy \n     \n    \n      Review of Scientific Instruments  ·  2016'
quote 3: MATCH_EXACT [12368..12701] 'Srivastava, J., Curd, M. E., Yao, Y., Holroyd, N. J. H., Shanthraj, P., Singh, S. B., Mandal, S., Prangnell, P. B. and Burnett, T. L. Effect of quench- and age-induced grain boundary η-phase precipitates on hydrogen environmentally induced cracking (H-EIC) behaviour of AA7085 alloy in humid air. Journal of Materials Science. (2026)'

reasoning

{
 "summary": [
  "**Evaluating contradictions**\n\nI’m working on determining if there's a contradiction here. The artifact doesn’t seem to support any broad absence or current claims. The engine text actually supports the collection and titles presented, but it feels unrelated to the 2026 work cited, and there’s no clear completeness. It appears that the grounding reason justifies the catalogue displayed, but it doesn’t fully address the no-study claim. It's a bit puzzling, and I want to make sure I interpret this correctly!"
 ]
}

output

{
 "accepted": true,
 "reason": "The grounding verifies the page’s description and displayed publication titles, but it does not establish catalogue completeness, currency through 2026, or the absence of the specified interlaboratory study; the 2026 item is unrelated citing work. It therefore does not contradict the step, though it is not probative of the broad absence claim."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You extract the exact source text a proof step rests on — FROM THE PAGE TEXT
PROVIDED IN THE PROMPT. The engine fetched that text itself and will align
every quote you return against exactly those bytes, token-by-token (bounded
tolerance for whitespace, casing, and typographic punctuation — never
paraphrase, never quote from memory). A separate analyst then judges whether
the engine-verified spans actually license the step.

# Goal
From the provided page text, put in `quotes` the substring(s) that state the
result the step invokes, copied from the page text as-is.

`claim_mapping`: one or two sentences on how the quotes license this step's
BEFORE -> AFTER transformation — including what they do NOT cover, if the
justification claims more than the source states.

# Success criteria
- Every quote is copied from the provided text, not composed or recalled.
- Quotes are the minimal spans that state the relied-on fact — not whole
  paragraphs, not fragments too short to assert anything. Prefer plain-prose
  statements; avoid regions mangled by leftover markup.
- If a multi-part theorem is involved, quote enough that cherry-picking
  would be visible.

# If the page does not state it
If the provided text does not contain what the step attributes to the
source, return your best honest extraction anyway (the nearest relevant
passage) and say in `claim_mapping` that it does not support the claim — the
analyst, not you, decides whether that is a contradiction.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Step 4 whose citation needs quoting:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']
  Justification: The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))

Source page (fetched by the engine from https://pmc.ncbi.nlm.nih.gov/articles/PMC11448745/):
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Philos Trans A Math Phys Eng Sci
. 2024 Jun 3;382(2274):20230257. doi: 10.1098/rsta.2023.0257





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Search in PubMed


View in NLM Catalog


Add to search







Developing the OpenFlexure Microscope towards medical use: technical and social challenges of developing globally accessible hardware for healthcare


Joe Knapper


Joe Knapper




1

University of Glasgow, Glasgow, UK



Conceptualization, Investigation, Methodology, Validation, Writing – original draft, Writing – review and editing


Find articles by Joe Knapper




1,✉, Freya Whiteford


Freya Whiteford




1

University of Glasgow, Glasgow, UK



Investigation, Methodology, Writing – review and editing


Find articles by Freya Whiteford




1, Daniel Rosen


Daniel Rosen




2

Baylor College of Medicine, Houston, Texas, USA



Funding acquisition, Investigation, Methodology, Resources, Supervision, Validation, Writing – review and editing


Find articles by Daniel Rosen




2, William Wadsworth


William Wadsworth




3

Department of Physics, University of Bath, Bath, UK



Formal analysis, Investigation, Methodology, Project administration, Supervision, Writing – review and editing


Find articles by William Wadsworth




3, Julian Stirling


Julian Stirling




4

Foxhill Engineering, Bath, UK



Investigation, Methodology, Software, Validation, Writing – review and editing


Find articles by Julian Stirling




4, Catherine Mkindi


Catherine Mkindi




5

Ifakara Health Institute, Ifakara, Tanzania



Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Validation, Writing – review and editing


Find articles by Catherine Mkindi




5, Joram Mduda


Joram Mduda




5

Ifakara Health Institute, Ifakara, Tanzania



Data curation, Investigation, Methodology, Validation, Writing – review and editing


Find articles by Joram Mduda




5, Valerian L Sanga


Valerian L Sanga




6

Bongo Tech and Research Labs, Dar es Salaam, Tanzania



Conceptualization, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Writing – review and editing


Find articles by Valerian L Sanga




6, Paul T Nyakyi


Paul T Nyakyi




6

Bongo Tech and Research Labs, Dar es Salaam, Tanzania



Data curation, Formal analysis, Investigation, Methodology, Resources, Validation


Find articles by Paul T Nyakyi




6, Thomas Hervé Mboa Nkoudou


Thomas Hervé Mboa Nkoudou




7

Mboalab and African Higher Institute of Open Science and Hardware (AHIOSH), Yaounde, Cameroon



Find articles by Thomas Hervé Mboa Nkoudou




7, Elisée Jafsia


Elisée Jafsia




7

Mboalab and African Higher Institute of Open Science and Hardware (AHIOSH), Yaounde, Cameroon



Find articles by Elisée Jafsia




7, Stephane Fadanka


Stephane Fadanka




7

Mboalab and African Higher Institute of Open Science and Hardware (AHIOSH), Yaounde, Cameroon



Find articles by Stephane Fadanka




7, Kelsey Hummel


Kelsey Hummel




8

MD Anderson Cancer Centre, Houston, Texas, USA



Find articles by Kelsey Hummel




8, Sharmila Anandasabapathy


Sharmila Anandasabapathy




2

Baylor College of Medicine, Houston, Texas, USA



Find articles by Sharmila Anandasabapathy




2, Richard Bowman


Richard Bowman




1

University of Glasgow, Glasgow, UK



Find articles by Richard Bowman




1





Author information


Article notes


Copyright and License information










1

University of Glasgow, Glasgow, UK





2

Baylor College of Medicine, Houston, Texas, USA





3

Department of Physics, University of Bath, Bath, UK





4

Foxhill Engineering, Bath, UK





5

Ifakara Health Institute, Ifakara, Tanzania





6

Bongo Tech and Research Labs, Dar es Salaam, Tanzania





7

Mboalab and African Higher Institute of Open Science and Hardware (AHIOSH), Yaounde, Cameroon





8

MD Anderson Cancer Centre, Houston, Texas, USA






One contribution of 6 to a Theo Murphy meeting issue ‘Open, reproducible hardware for microscopy’.




✉
Corresponding author.






Roles



Joe Knapper: Conceptualization, Investigation, Methodology, Validation, Writing – original draft, Writing – review and editing




Freya Whiteford: Investigation, Methodology, Writing – review and editing




Daniel Rosen: Funding acquisition, Investigation, Methodology, Resources, Supervision, Validation, Writing – review and editing




William Wadsworth: Formal analysis, Investigation, Methodology, Project administration, Supervision, Writing – review and editing




Julian Stirling: Investigation, Methodology, Software, Validation, Writing – review and editing




Catherine Mkindi: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Validation, Writing – review and editing




Joram Mduda: Data curation, Investigation, Methodology, Validation, Writing – review and editing




Valerian L Sanga: Conceptualization, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Writing – review and editing




Paul T Nyakyi: Data curation, Formal analysis, Investigation, Methodology, Resources, Validation








Received 2023 Oct 11; Accepted 2024 Feb 23; Collection date 2024 Jun.







© 2024 The Authors.


Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.


PMC Copyright notice






PMCID: PMC11448745  PMID: 38826050









Abstract


The OpenFlexure Microscope is an accessible, three-dimensional-printed robotic microscope, with sufficient image quality to resolve diagnostic features including parasites and cancerous cells. As access to lab-grade microscopes is a major challenge in global healthcare, the OpenFlexure Microscope has been developed to be manufactured, maintained and used in remote environments, supporting point-of-care diagnosis. The steps taken in transforming the hardware and software from an academic prototype towards an accepted medical device include addressing technical and social challenges, and are key for any innovation targeting improved effectiveness in low-resource healthcare.


This article is part of the Theo Murphy meeting issue 'Open, reproducible hardware for microscopy'.



Keywords: global health, open source, pathology, microscopy




1. 
 Introduction


First announced in 2016, the OpenFlexure Microscope is a three-dimensional-printed, accessible microscope capable of automatically moving, focusing and capturing digital images of samples. The hardware (shown in figure 1) and controlling software are open source, meaning users are permitted to manufacture, use, modify and sell the designs without restriction from patents or copyright. This has led to international uptake of the project, with use on every continent for a range of applications. Spin-out projects, including the OpenFlexure Block Stage [2] and OpenFlexure Delta Stage [3], also use three-dimensional-printed monolithic designs to produce high-precision flexure hinges. Other research groups within the rapidly developing community have adapted the OpenFlexure Microscope for imaging modes including super-resolution microscopy, and optical-sectioning microscopy [4,5].


Figure 1. 






Open in a new tab


An exploded view of the OpenFlexure Microscope version 6.1.5, reproduced from [1] under the CC-BY-SA licence.

Optical microscopes are a key device in medical diagnostics, used for the identification and characterization of dozens of conditions, including cancer, sexually transmitted infections and parasitic infections [6]. The World Health Organization (WHO) describes manual optical microscopy as the ‘gold standard’ of malaria diagnosis [7]. Malaria is a disease caused by Plasmodium parasites in blood, and—despite prognosis being generally positive if diagnosed early—is responsible for over 500 000 deaths per year, with the majority in sub-Saharan Africa. The WHO identifies rapid, accurate diagnoses as the most effective method for reducing the effect of the disease. A blood sample, smeared and stained with a Giemsa stain before manual examination under a light microscope, is the most effective way to diagnose malaria. In addition to the sensitivity and specificity of the method, it can also be performed at the point of care, is versatile (can be used to diagnose other conditions or other sample types) and the cost per test scales favourably.


However, limited access to high-quality, well-maintained microscopes and trained users restricts the accessibility of these tests. A survey of Tanzanian health clinics reported that only 42% had access to a light microscope for malaria diagnosis, dropping to just 20% of public health facilities [8]. Furthermore, there is a worldwide workforce shortage across pathology services [9]. This limited access makes reliable diagnosis less common, and necessitates unreliable procedures. Patients are frequently required to travel to health centres for testing and treatment. Varela et al. identify accessibility of reliable transport, the associated financial burden and the duration of the journey as barriers to accessing life-saving treatment [10]. These journeys can involve travelling by car, public transport, bicycles, on foot or some combination thereof, and become less accessible as distance to the healthcare facility increases. The limited accessibility of testing has also led several African countries to operate a ‘hub and spoke’ model for diagnosis, in which samples are collected at local clinics, then transported by motorcycle courier to a central laboratory for testing [11]. This introduces delays and the possibility of sample damage or loss, reducing confidence in local healthcare. This demonstrates the opportunity for improving effectiveness by distributing diagnostic devices to regional health centres.


Improving the accessibility of local diagnosis requires the procurement of high-quality, reliable microscopes. Hardware donations attempt to improve accessibility, but often go unused owing to the need for consumables, maintenance, spare parts and training. We argue that a better solution is the local manufacture, maintenance and use of automated microscopes, not only increasing the availability of devices, but also supporting clinics by allowing the automation of workflow.


This has motivated the development of the OpenFlexure Microscope towards supporting healthcare in low-resource settings. Target environments include the diagnosis of malaria in Tanzania, and oesophageal cancer in Brazil. OpenFlexure Microscope deployment in a teaching hospital in Rwanda is planned in early 2024, with the aim of making diagnosis and education more accessible. While these applications vary in terms of location, sample type and diagnosis procedure, the common challenges are the same. Microscope resolution and contrast must be sufficient to identify the features of interest, and automated sample scanning must be reliable, allowing healthcare workers to perform other manual microscope tasks with confidence. The design and workflow must be reliable and simple, allowing use by non-specialists with a range of backgrounds. Design decisions have been directed by the long-term objective of obtaining medical certification for the OpenFlexure Microscope.


Medical certification is awarded for an assembled product; not underlying design. As such, work is ongoing towards medical certification for sayansiScope, the OpenFlexure Microscope as manufactured in Tanzania by Bongo Tech and Research Labs. This would be the first complete digital diagnostic system manufactured in Tanzania, and would represent a significant step towards local sustainability in healthcare. This aligns with UN Sustainable Development Goals 3, 8, 9 and 12, for Good Health and Well-Being; Decent Work and Economic Growth; Industry, Innovation and Infrastructure; and Responsible Consumption and Production [12].


To maximize uptake and confidence in the OpenFlexure Microscope, we are working to align the design and documentation to the standards required for medical device production. The ISO Standard 13485, ‘Medical devices—Quality management systems—Requirements for regulatory purposes’, is a regulatory standard requiring systematic consideration of the applications, limits and risks associated with a device [13]. This standard covers the full life cycle of a medical device, ‘from the initial conception to final decommissioning and disposal’, and requires documentation of decisions and procedures.


The requirements for becoming medically compliant and suitable for use have been identified and addressed by co-developing the microscope between a range of specialities and locations. Development towards medical use has involved contributions from engineers, physicists, life scientists, computer scientists and healthcare professionals. While the OpenFlexure core team is based in the United Kingdom, the microscope has been co-developed with Tanzanian medical partners and engineering partners from Tanzania, Cameroon and Ghana, with feedback from global health workers based at the Baylor College of Medicine and MD Anderson Cancer Centre, Texas, USA. This has ensured suitability for the end users, based on their requirements and experience.


As the OpenFlexure Microscope continues to be validated in clinical settings, we show how this application has directed the project. We identify steps taken, as well as future work required to ensure utility. These challenges and decisions can broadly be split into technical and social categories, as both are essential for acceptance in healthcare environments.



2. 
 Technical challenges and solutions



(a). Optical performance and automation


The OpenFlexure Microscope is designed to be printed, assembled and used in any environment. The monolithic plastic body can be printed on the lowest quality hobbyist printers, and additional parts have been selected for their reliable supply chains and low cost. A Raspberry Pi computer controls the camera and motors, allowing samples to be scanned automatically. The device can be controlled directly through a mouse and keyboard, through OpenFlexure Connect (a custom-built GUI) or through a range of programming languages including Python and Blockly.


Image-based autofocusing is performed based on the sharpness of the field of view through a range of 
z
 positions, measured according to the JPEG file size of the camera stream. Using a 100
×
 objective magnification, the reduced depth of field necessitates additional steps in autofocusing, using a self-correcting closed-loop approach [14].


The OpenFlexure Microscope supports a range of RMS-threaded objectives, ranging from 0.25 NA to 1.25 NA. Each level of optical power is suitable for different applications and diagnoses, and so components must be selected according to specific use. For the diagnosis of cancer in oesophagus biopsies or pap smears, a 0.25 NA (10
×
) objective is sufficient to give an overview of the sample, while 0.4 NA (20
×
) or 0.65 NA (40
×
) may be required to resolve the finest details. For resolving malaria-causing Plasmodium parasites in a blood smear, an oil-immersion 1.25 NA (100
×
) objective is required. The inclusion of index-matching oil and a sub-micron depth of field present additional challenges for automating the imaging of subcellular structures.


While objectives can be swapped on the current OpenFlexure Microscope, this requires removing the sample and unscrewing the objective from within the inverted microscope body. Feedback from pathologists indicates the need for the objectives to be easier to swap, without disturbing the sample position. This has motivated development of an upright microscope design with a swapple objective.


This is achieved through the inclusion of a magnetically constrained, interchangeable three-dimensional-printed mount. There are technical challenges associated with constraining the printed mount sufficiently to achieve a reliabe co-incident positioning of the field of view and the sample. While the inclusion of magnets and other fixings can improve accuracy, we also ensure repeatability by using the camera feed to estimate displacement between objectives; this allows the microscope to automatically correct its own position. The use of camera feedback to improve performance, rather than relying on perfect hardware performance, is a common theme in this project. This self-correcting, closed-loop approach allows high performance without adding to the cost or complexity of the physical device.



(b). Calibration


Projects with distributed manufacturing are dependent on diverse levels of supply chains, experience and equipment quality to ensure the final product is consistent, regardless of location. For small-scale projects devices can be manually verified; however, this solution scales poorly as the user base grows. This has necessitated the development of a range of microscope self-certification tools. Utilizing the camera to give feedback on image quality, stage mechanics and illumination alignment allows the software to correct for minor differences between devices, while major discrepancies can be identified and corrected before the device is used for patient samples.


As shown in figure 2, the OpenFlexure Microscope has been assembled or used in over 45 countries. While a range of microscope calibration procedures are available, they often rely on expensive test targets or specialist interpretation of data [16,17]. To ensure that cost and training do not become additional barriers to entry, OpenFlexure software performs its range of calibration and self-certification procedures on accessible targets.


Figure 2. 






Open in a new tab


A map of the countries in which the OpenFlexure Microscope has been built or used, according to users in an OpenFlexure forum thread [15].

While calibration of the illumination and camera sensor can be performed without a sample, and stage-to-image calibration can be performed using any sample with obvious features, resolution and physical distance can only be assessed from a target with a known feature size. Our custom calibration software (MICAT) [18] uses a USAF 1951 resolution target (approximate cost £200, from a range of suppliers), which has a pattern of decreasingly spaced periodic grates. Determining the pixel size from images of these features of known size allows calibration between motor position, image coordinates and physical sample location. Capturing images of a large slanted edge allows estimation of the line spread function (a one-dimensional analogue to the point spread function). This resolution metric can identify a poorly assembled microscope, advising the user that the resolution limit may be higher than the features they need to examine.


In the case that these calibration steps indicate insufficient performance, the software can advise users of possible causes and suggest next steps, including returning the microscope to the manufacturer for maintenance. As a low-cost, modular product, the system can be repaired or replaced locally, aligning with the ISO 13485 standard requirement of considering the end of life of a medical device. This is in contrast with many proprietary systems donated from the ‘Global North’, which can restrict maintenance and repairs.


We suggest a workflow in which each newly assembled device is fully calibrated, with the most essential characteristics also being automatically re-tested at the start of each workday. The results of each calibration run are archived, allowing full traceability between certification and medical scans. This would be part of the basis of a risk-management procedure, required for medical devices by ISO 14971, ‘Medical devices—Application of risk management to medical devices’ [19]. This would ensure that issues are identified and the user informed before they can affect patient outcomes.


While not critical for diagnosis, other performance-improving monitoring of the microscope can be carried out during ongoing scans. The motion of the translation stage of the OpenFlexure Microscope follows a sphere-cap, and so the parasitic motion in 
z
 for an 
xy
 move can be predicted. Therefore, a focus map of the sample can speed up image acquisition. Measuring how long the stage takes to settle after movements allows images to be collected as soon as the system is stable. More accurate movement and indentification of the limits of the range of motion can be achieved by performing closed-loop movements; using the camera stream to feedback on the success of each movement. While these steps cannot replace the knowledge of experienced users, they allow new users to have confidence in the device performance.




3. 
 Organization of a distributed project


Managing and directing a distributed, open project requires active collaboration and networking; the publication of source code and designs is only the first step in making the project accessible. How to best manage a collaborative project is both a technical and social problem, as users require both technical skills and motivation to share their work. Any barrier to the free sharing of knowledge and experience can decrease th
---

output

{
 "quotes": [
  "This has necessitated the development of a range of microscope self-certification tools. Utilizing the camera to give feedback on image quality, stage mechanics and illumination alignment allows the software to correct for minor differences between devices, while major discrepancies can be identified and corrected before the device is used for patient samples.",
  "While calibration of the illumination and camera sensor can be performed without a sample, and stage-to-image calibration can be performed using any sample with obvious features, resolution and physical distance can only be assessed from a target with a known feature size. Our custom calibration software (MICAT) [18] uses a USAF 1951 resolution target (approximate cost £200, from a range of suppliers), which has a pattern of decreasingly spaced periodic grates.",
  "We suggest a workflow in which each newly assembled device is fully calibrated, with the most essential characteristics also being automatically re-tested at the start of each workday. The results of each calibration run are archived, allowing full traceability between certification and medical scans."
 ],
 "claim_mapping": "These passages support that Knapper et al. describe self-certification and a proposed calibration workflow covering illumination/camera calibration, stage-to-image calibration, and MICAT resolution calibration with a USAF 1951 target. The provided page text does not include the claimed data-accessibility statement that the article has no additional data."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You decide whether a judge's legitimate rejection can be resolved
by invoking a single standard, domain-level convention. This is
the LAST chance for a proof step; if you lift, the step becomes
accepted-under-assumption and its convention is recorded in the
proof's list of added assumptions. If you don't lift, the step
stays rejected and the proof is not verified.

Be VERY conservative. A convention qualifies ONLY if ALL of:

1. ASYMMETRIC DEFAULT: the opposite of this assumption would
   have to be explicitly stated by the author if they meant
   it. Practitioners invoke this default automatically when
   the problem is silent about it. If BOTH the assumption and
   its opposite are equally plausible when the problem omits
   the detail, NEITHER is a convention — the problem is
   genuinely ambiguous between them, and you must not lift.

2. Verifiable source: the assumption is either explicitly
   stated as default in a published reference, or pervasively
   used without statement in published references for this
   problem class. Provide a URL or textbook+section. Use web
   search to verify.

3. Once added as a premise, fully justifies the rejected step
   — the rejection reason must disappear when the convention
   is added.

Do NOT lift: specific numeric values, instantiated parameters,
interpretations where multiple equally-plausible defaults
exist, or convenience simplifications that the author might
reasonably not have intended.

Required output:
  can_lift: boolean — true only if all three criteria met
  convention: the convention stated as an explicit added premise
  source: published reference (URL or textbook+section)
  reasoning: brief explanation of why all three criteria are met,
             or why they aren't

When in doubt, can_lift = false. The benchmark's trustworthiness
depends on you being strict. Treat this the same way you'd treat
a decision to publish: would a skeptical reader of a paper accept
this convention as canonical?

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 5 being evaluated:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  Justification type: computation
  Justification: A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.

Judge's rejection reason:
1. The step assumes Knapper et al. contain no comparative three-laboratory data, but the previous state establishes only that the paper describes a calibration workflow and says there are “no additional data.” A data-accessibility statement of that kind does not imply that no comparative measurements are reported within the article itself.
2. The previous state does not explicitly establish that its summary of Knapper et al. is exhaustive. Listing several calibration procedures does not by itself rule out a three-laboratory dataset elsewhere in the paper.
3. Therefore, although the conditional claim that a workflow without comparative data cannot establish interlaboratory agreement is logically correct, the required antecedent—absence of comparative laboratory data—has not been established in the previous state.

Pedantry already confirmed this rejection is legitimate:
The rejection is legitimate. The inference requires the factual antecedent that Knapper et al. report no comparative three-laboratory dataset. The previous state does not establish that: “no additional data” does not exclude data presented within the article, and a non-exhaustive description of its calibration workflow does not rule out comparative results elsewhere. This is a plausible substantive evidence-reading error, not merely a demand for extra rigor.

Is there a single standard, citable, domain-wide convention that — if added as an explicit premise — would fully justify this step and resolve the judge's objection?

reasoning

{
 "summary": [
  "**Searching for data availability standards**\n\nI recognize we need to conduct a search to find the exact JSON schema. It seems like determining whether there's a falsehood is crucial. There’s no convention that says summaries are exhaustive, and no additional data implies there might be no in-article data. I also think we need to look for a source, perhaps from FAIR or a similar data availability standard to clarify the requirements for data availability statements. Let's narrow down our search for that information!"
 ]
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "official journal data availability statement no additional data article supporting data meaning",
   "Royal Society data accessibility statement no additional data article policy"
  ],
  "query": "official journal data availability statement no additional data article supporting data meaning"
 }
}

reasoning

{
 "summary": [
  "**Considering JSON specifications**\n\nI need to ensure I have the exact JSON format, maybe looking into something like the Royal Society policy for guidance. It feels important to explain that there’s no asymmetric default here; I'm dealing with a factual paper-content question that requires careful inspection. The opposite situation is also equally possible. Perhaps I could consider leaving the convention empty, maybe with \"None.\" I really want to make sure the JSON is valid!"
 ]
}

output

{
 "can_lift": false,
 "convention": "None. A data-accessibility statement saying that an article contains “no additional data” cannot conventionally be treated as an exhaustive statement that the article reports no comparative measurements.",
 "source": "Royal Society, “Data sharing”: https://royalsociety.org/journals/ethics-policies/data-sharing-mining/",
 "reasoning": "Royal Society policy defines data-accessibility statements as identifying access to data, code, and materials supporting results in the article. It does not make such statements exhaustive descriptions of results reported within the article. Nor is there a domain-wide convention that a partial summary of calibration procedures exhausts a paper’s contents. The presence and absence of a three-laboratory dataset are factual alternatives requiring inspection of the complete article; neither is an asymmetric default. Thus no standard convention supplies the missing antecedent, and the judge’s objection remains."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall.

You decide whether a judge's legitimate rejection can be resolved
by invoking a single standard, domain-level convention. This is
the LAST chance for a proof step; if you lift, the step becomes
accepted-under-assumption and its convention is recorded in the
proof's list of added assumptions. If you don't lift, the step
stays rejected and the proof is not verified.

Be VERY conservative. A convention qualifies ONLY if ALL of:

1. ASYMMETRIC DEFAULT: the opposite of this assumption would
   have to be explicitly stated by the author if they meant
   it. Practitioners invoke this default automatically when
   the problem is silent about it. If BOTH the assumption and
   its opposite are equally plausible when the problem omits
   the detail, NEITHER is a convention — the problem is
   genuinely ambiguous between them, and you must not lift.

2. Verifiable source: the assumption is either explicitly
   stated as default in a published reference, or pervasively
   used without statement in published references for this
   problem class. Provide a URL or textbook+section. Use web
   search to verify.

3. Once added as a premise, fully justifies the rejected step
   — the rejection reason must disappear when the convention
   is added.

Do NOT lift: specific numeric values, instantiated parameters,
interpretations where multiple equally-plausible defaults
exist, or convenience simplifications that the author might
reasonably not have intended.

Required output:
  can_lift: boolean — true only if all three criteria met
  convention: the convention stated as an explicit added premise
  source: published reference (URL or textbook+section)
  reasoning: brief explanation of why all three criteria are met,
             or why they aren't

When in doubt, can_lift = false. The benchmark's trustworthiness
depends on you being strict. Treat this the same way you'd treat
a decision to publish: would a skeptical reader of a paper accept
this convention as canonical?

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Full proof:
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.

Step 6 being evaluated:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]
  Justification type: citation
  Justification: Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))

Judge's rejection reason:
1. The catalogue is not represented as exhaustive. Its “Citing publications” section explicitly asks users to notify the project so publications can be added, so absence from this list cannot establish absence of a qualifying peer-reviewed study. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
2. “Current through work listed for 2026” is unsupported and misleading. The page lists two 2026 papers only under “Citing publications,” while the project’s own “Publications and conferences” list ends in 2024; inclusion of some 2026 citations does not demonstrate comprehensive coverage through August 31, 2026. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
3. The catalogue supplies mainly bibliographic entries and titles. It does not document that every listed paper was inspected for measurements from three laboratories, all four quantities, certified targets, and uncertainty budgets. Therefore it cannot by itself justify the detailed content-based negative claim.
4. The page combines journal articles, conference papers, presentations, preprints, and citing publications, including an F1000Research item whose displayed peer-review status includes one approval and one non-approval. Thus the citation does not provide a clean, defined catalogue of exclusively peer-reviewed entries matching the claim’s characterization. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))

Pedantry already confirmed this rejection is legitimate:
The rejection is legitimate. The cited page expressly presents a user-notified collection rather than an exhaustive bibliography, mixes project outputs with citing publications and nonuniform publication types/statuses, and does not show that every listed work was inspected for the detailed four-quantity, three-laboratory uncertainty comparison. Its two 2026 citing entries also do not support claiming comprehensive coverage through August 31, 2026. Therefore the catalogue alone cannot establish the asserted absence of any qualifying peer-reviewed study.

Is there a single standard, citable, domain-wide convention that — if added as an explicit premise — would fully justify this step and resolve the judge's objection?

reasoning

{
 "summary": [
  "**Searching for JSON schema details**\n\nI need to produce the exact JSON schema, and since I was instructed to browse, I have to check for that information. The question arises whether conventions could resolve the issues with something being absent from the catalogue. It’s pretty clear that they can't. So, I should probably confirm by searching for the source page and opening it to find the necessary details. Let's see what I can uncover!"
 ]
}

web_search

{
 "action": {
  "type": "open_page",
  "url": "https://openflexure.gitlab.io/about/publications"
 }
}

web_search

{
 "action": {
  "type": "search",
  "queries": [
   "PRISMA 2020 statement identify all eligible studies comprehensive search bibliographic databases official",
   "Cochrane Handbook searching for studies comprehensive search all relevant studies"
  ],
  "query": "PRISMA 2020 statement identify all eligible studies comprehensive search bibliographic databases official"
 }
}

output

{
 "can_lift": false,
 "convention": "",
 "source": "OpenFlexure Academic Publications catalogue, https://openflexure.gitlab.io/about/publications; Cochrane Handbook for Systematic Reviews of Interventions, Chapter 4, https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-04",
 "reasoning": "No canonical convention treats a project-maintained, user-notified bibliography as exhaustive, or permits bibliographic titles alone to establish that no qualifying study exists. The catalogue expressly invites users to report omitted publications, mixes publication types and review statuses, and does not document full-text eligibility assessment. Standard evidence-review practice instead requires a comprehensive, reproducible search and content-based screening. Adding an exhaustiveness premise would be a source-specific factual assumption—not an asymmetric domain default—and would still not establish that every entry was inspected for all four measurements, certified targets, three laboratories, and uncertainty budgets."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You are the contradiction check on a deterministic grounding. An independent
agent produced an artifact for one proof step (a sympy program, a Lean file,
or a source extraction); the ENGINE then executed or verified it first-hand.
You see the artifact and the engine-witnessed output, and return a verdict
only — never fixes, never advice.

Your verdict gates a hard rejection: `accepted: false` cannot be overturned
downstream, so it must mean a genuine, demonstrated contradiction.

# Decide

Reject (`accepted: false`) only when BOTH hold:
1. The artifact faithfully checks what the step claims — same quantities, same
   relation, computed rather than copied; a checked Lean statement says what
   the step says; verified quotes are about the fact the step relies on.
2. The engine-witnessed output contradicts the step's claimed transformation —
   a different value, a failed relation, a checked Lean statement proving the
   NEGATION of the step's claim, or source text that states something
   incompatible with what the step attributes to it. A proved negation counts
   as faithful for criterion 1: it addresses exactly the step's claim.

Everything else accepts (`accepted: true`), because acceptance is the neutral
outcome — the step still faces its own judge:
- Representation differences are NOT contradictions: 2/4 vs 1/2, sqrt(2)/2 vs
  1/sqrt(2), reordered terms, equivalent phrasing, print formatting.
- An artifact that is not probative — it hardcodes the answer, computes
  something other than the step's claim, states a weaker/stronger theorem, or
  quotes text unrelated to the claim — accepts, with a reason saying the
  grounding was not probative.
- Output you cannot decisively map onto the step's claim accepts.

For extraction groundings, the output lists the fetched source (url + sha256
provenance header) and each quote's alignment: status, char interval, and the
aligned source span. Judge from the SPAN text — that is the source's own
wording, engine-witnessed; the author's quote is only the search key. A
MATCH_FUZZY span whose actual wording states something incompatible with what
the step attributes to the source is exactly the contradiction to reject.

# Reason field
One or two sentences. On rejection, quote the engine-witnessed output verbatim
against the step's claimed value — the repair loop sees only your reason, so
the deterministic evidence must be in it. On acceptance, say what the grounding
established (or why it was not probative). Verdict only: never suggest how to
fix the step.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Step 2 whose grounding is under review:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']
  Justification type: citation
  Justification: Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))

Artifact (produced by an independent grounding agent):
These passages provide only nearby statements about optical aberration mitigation and qualitative resolving performance. The supplied page text ends before section 2.2 and does not state the claimed USAF-target method, 480 nm FWHM, central-50% result, field-curvature edge degradation, lens-shading-table correction, uncertainty budgets, or absence of a three-laboratory comparison.
quote 1 (author): 'The high-quality optics module makes use of achromatic objectives and an achromatic tube lens to minimize chromatic aberrations. While narrow-band illumination sources would help further minimize chromatic aberrations, full-color white light imaging is typically required for our applications such as blood parasite imaging (section 2.1.1) and graphene flake imaging (section 2.1.2). Nevertheless, by introducing achromatic optics, the dominant chromatic effect becomes the chief ray angle color mixing, which can be largely mitigated with software calibration [19].'
quote 2 (author): 'In this configuration, individual red blood cells, with dimensions on the order of microns, are clearly resolved. A ring-form trophozoite of Plasmodium falciparum within a red blood cell is highlighted in the figure inset (contrast has been digitally enhanced for clarity by increasing brightness and gamma). Despite being only 1 µm to 2 µm across, the morphology of these ring-form parasites is also clearly resolved by the OFM.'

Engine-witnessed output:
source: https://pmc.ncbi.nlm.nih.gov/articles/PMC7249832/ sha256=143658fd7d0a8924f22f4f2745e2f5e68522e4239cbe6ce374c67589b0981f4b 30000 chars [truncated]
quote 1: MATCH_EXACT [19207..19773] 'The high-quality optics module makes use of achromatic objectives and an achromatic tube lens to minimize chromatic aberrations. While narrow-band illumination sources would help further minimize chromatic aberrations, full-color white light imaging is typically required for our applications such as blood parasite imaging (section 2.1.1) and graphene flake imaging (section 2.1.2). Nevertheless, by introducing achromatic optics, the dominant chromatic effect becomes the chief ray angle color mixing, which can be largely mitigated with software calibration [19].'
quote 2: MATCH_EXACT [23532..23961] 'In this configuration, individual red blood cells, with dimensions on the order of microns, are clearly resolved. A ring-form trophozoite of Plasmodium falciparum within a red blood cell is highlighted in the figure inset (contrast has been digitally enhanced for clarity by increasing brightness and gamma). Despite being only 1 µm to 2 µm across, the morphology of these ring-form parasites is also clearly resolved by the OFM.'

output

{
 "accepted": true,
 "reason": "The extracted passages discuss chromatic-aberration mitigation and qualitative parasite resolving performance, but do not address the claimed USAF-target measurement, 480 nm FWHM, central-field coverage, field curvature, vignetting correction, uncertainty budgets, or laboratory count. The grounding is therefore not probative of the step's specific claims and establishes no contradiction."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You are the contradiction check on a deterministic grounding. An independent
agent produced an artifact for one proof step (a sympy program, a Lean file,
or a source extraction); the ENGINE then executed or verified it first-hand.
You see the artifact and the engine-witnessed output, and return a verdict
only — never fixes, never advice.

Your verdict gates a hard rejection: `accepted: false` cannot be overturned
downstream, so it must mean a genuine, demonstrated contradiction.

# Decide

Reject (`accepted: false`) only when BOTH hold:
1. The artifact faithfully checks what the step claims — same quantities, same
   relation, computed rather than copied; a checked Lean statement says what
   the step says; verified quotes are about the fact the step relies on.
2. The engine-witnessed output contradicts the step's claimed transformation —
   a different value, a failed relation, a checked Lean statement proving the
   NEGATION of the step's claim, or source text that states something
   incompatible with what the step attributes to it. A proved negation counts
   as faithful for criterion 1: it addresses exactly the step's claim.

Everything else accepts (`accepted: true`), because acceptance is the neutral
outcome — the step still faces its own judge:
- Representation differences are NOT contradictions: 2/4 vs 1/2, sqrt(2)/2 vs
  1/sqrt(2), reordered terms, equivalent phrasing, print formatting.
- An artifact that is not probative — it hardcodes the answer, computes
  something other than the step's claim, states a weaker/stronger theorem, or
  quotes text unrelated to the claim — accepts, with a reason saying the
  grounding was not probative.
- Output you cannot decisively map onto the step's claim accepts.

For extraction groundings, the output lists the fetched source (url + sha256
provenance header) and each quote's alignment: status, char interval, and the
aligned source span. Judge from the SPAN text — that is the source's own
wording, engine-witnessed; the author's quote is only the search key. A
MATCH_FUZZY span whose actual wording states something incompatible with what
the step attributes to the source is exactly the contradiction to reject.

# Reason field
One or two sentences. On rejection, quote the engine-witnessed output verbatim
against the step's claimed value — the repair loop sees only your reason, so
the deterministic evidence must be in it. On acceptance, say what the grounding
established (or why it was not probative). Verdict only: never suggest how to
fix the step.

user

Problem: For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/


Step 4 whose grounding is under review:
  Previous state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']
  New state: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']
  Justification type: citation
  Justification: The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))

Artifact (produced by an independent grounding agent):
These passages support that Knapper et al. describe self-certification and a proposed calibration workflow covering illumination/camera calibration, stage-to-image calibration, and MICAT resolution calibration with a USAF 1951 target. The provided page text does not include the claimed data-accessibility statement that the article has no additional data.
quote 1 (author): 'This has necessitated the development of a range of microscope self-certification tools. Utilizing the camera to give feedback on image quality, stage mechanics and illumination alignment allows the software to correct for minor differences between devices, while major discrepancies can be identified and corrected before the device is used for patient samples.'
quote 2 (author): 'While calibration of the illumination and camera sensor can be performed without a sample, and stage-to-image calibration can be performed using any sample with obvious features, resolution and physical distance can only be assessed from a target with a known feature size. Our custom calibration software (MICAT) [18] uses a USAF 1951 resolution target (approximate cost £200, from a range of suppliers), which has a pattern of decreasingly spaced periodic grates.'
quote 3 (author): 'We suggest a workflow in which each newly assembled device is fully calibrated, with the most essential characteristics also being automatically re-tested at the start of each workday. The results of each calibration run are archived, allowing full traceability between certification and medical scans.'

Engine-witnessed output:
source: https://pmc.ncbi.nlm.nih.gov/articles/PMC11448745/ sha256=69d4884ba578194233f16d008bdd175b1840bd9d13e214f88f88d552720cce8f 30000 chars [truncated]
quote 1: MATCH_EXACT [25649..26011] 'This has necessitated the development of a range of microscope self-certification tools. Utilizing the camera to give feedback on image quality, stage mechanics and illumination alignment allows the software to correct for minor differences between devices, while major discrepancies can be identified and corrected before the device is used for patient samples.'
quote 2: MATCH_EXACT [26634..27099] 'While calibration of the illumination and camera sensor can be performed without a sample, and stage-to-image calibration can be performed using any sample with obvious features, resolution and physical distance can only be assessed from a target with a known feature size. Our custom calibration software (MICAT) [18] uses a USAF 1951 resolution target (approximate cost £200, from a range of suppliers), which has a pattern of decreasingly spaced periodic grates.'
quote 3: MATCH_EXACT [28106..28408] 'We suggest a workflow in which each newly assembled device is fully calibrated, with the most essential characteristics also being automatically re-tested at the start of each workday. The results of each calibration run are archived, allowing full traceability between certification and medical scans.'

reasoning

{
 "summary": [
  "**Assessing contradictions**\n\nI need to assess a contradiction in the procedures. One step claims there’s no additional data, yet the artifact supports the first claim and states that the provided page has no data statement. It seems the engine's quotes don't contradict the idea of no data; they just aren't probative. I accept this because the grounding establishes the workflow. Also, the proposed self-certification seems fair, but the certified target isn't certified according to the USAF. That's okay."
 ]
}

output

{
 "accepted": true,
 "reason": "The source spans establish the described self-certification workflow, illumination/camera and stage-to-image calibration, and MICAT use of a USAF 1951 resolution target. They do not verify the separate claim that the article has no additional data, but this lack of support is not a contradiction."
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem.

You write the literature-search queries for one verification run, from its
digest: the question (a research proposal's hypothesis), the outcome, the
proof, and every audited claim with the checker's reason. You do not search.
An engine runs every query you return against OpenAlex (title, abstract and
full text of ~250M works) and records the exact URL, the total match count
and the top hits; the adjudicator reads those results, not your opinion.

Return one `searches` entry per claim worth testing:
- every absence claim the run relied on or failed on ("no study reports X",
  "X has not been measured", "no benchmark covers Y"), in the digest's words;
- the proposal's question itself: has it already been answered?

For each, `queries` is a ladder from broad to narrow, as many rungs as the
vocabulary needs. The broadest rung names the topic and must plausibly match
published work; each narrower rung adds a condition the claim turns on.
Cover the field's synonyms and named artefacts (tools, datasets, benchmarks,
versions) across rungs rather than inside one query. A ladder whose broad
rung matches nothing is uncalibrated and proves nothing, so prefer several
plain rungs to one long one.

Query syntax: whole words, stemmed; AND / OR / NOT (uppercase) and
parentheses; "double quotes" for phrases. `from_date` / `to_date` bound the
publication date (YYYY-MM-DD; "" for unbounded). `issns`: journal ISSNs to
restrict to, only when the claim names venues; otherwise [].

user

QUESTION:
For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/

OUTCOME: Declined budget_exhausted
DETAIL: step 1 [problem_given] judge: 1. The problem does not state that the measurements must be published; “published” is an added evidentiary premise.
2. The problem says “across three independent labs,” not “at least three independent laboratories.” Treating this as a minimum of three is an interpretation rather than a directly stated value.; step 1 extraction: The engine-witnessed problem statement says only “resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties”; it does not state the added requirement that the measurements be published.; step 5 [computation] judge: 1. The step assumes Knapper et al. contain no comparative three-laboratory data, but the previous state establishes only that the paper describes a calibration workflow and says there are “no additional data.” A data-accessibility statement of that kind does not imply that no comparative measurements are reported within the article itself.
2. The previous state does not explicitly establish that its summary of Knapper et al. is exhaustive. Listing several calibration procedures does not by itself rule out a three-laboratory dataset elsewhere in the paper.
3. Therefore, although the conditional claim that a workflow without comparative data cannot establish interlaboratory agreement is logically correct, the required antecedent—absence of comparative laboratory data—has not been established in the previous state.; step 6 [citation] judge: 1. The catalogue is not represented as exhaustive. Its “Citing publications” section explicitly asks users to notify the project so publications can be added, so absence from this list cannot establish absence of a qualifying peer-reviewed study. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
2. “Current through work listed for 2026” is unsupported and misleading. The page lists two 2026 papers only under “Citing publications,” while the project’s own “Publications and conferences” list ends in 2024; inclusion of some 2026 citations does not demonstrate comprehensive coverage through August 31, 2026. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
3. The catalogue supplies mainly bibliographic entries and titles. It does not document that every listed paper was inspected for measurements from three laboratories, all four quantities, certified targets, and uncertainty budgets. Therefore it cannot by itself justify the detailed content-based negative claim.
4. The page combines journal articles, conference papers, presentations, preprints, and citing publications, including an F1000Research item whose displayed peer-review status includes one approval and one non-approval. Thus the citation does not provide a clean, defined catalogue of exclusively peer-reviewed entries matching the claim’s characterization. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications)) [budget exhausted: formalizer]
PROOF (final round):
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.
AUDITED CLAIMS:
- [accepted] state 0: State 0 contains only “ANSWER,” which is an allowed goal placeholder, and it contains no added premises, conclusions, computations, or other unsupported content.
- [FAILED] step 1 [problem_given] judge: 1. The problem does not state that the measurements must be published; “published” is an added evidentiary premise.
2. The problem says “across three independent labs,” not “at least three independent laboratories.” Treating this as a minimum of three is an interpretation rather than a directly stated value.
- [FAILED] step 1 extraction: The engine-witnessed problem statement says only “resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties”; it does not state the added requirement that the measurements be published.
- [accepted] step 2 [citation] judge: The cited paper supports every added claim: section 2.2 derives a 480 nm PSF FWHM from an edge on a USAF resolution target, describes near-diffraction-limited performance over the central 50% of the field and decreased edge resolution caused by field curvature and aberration, and describes vignetting correction by overriding the lens-shading table. The paper contains no three-independent-laboratory comparison or associated uncertainty budgets. No hidden premise is introduced. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
- [accepted] step 2 extraction: The extracted passages discuss chromatic-aberration mitigation and qualitative parasite resolving performance, but do not address the claimed USAF-target measurement, 480 nm FWHM, central-field coverage, field curvature, vignetting correction, uncertainty budgets, or laboratory count. The grounding is therefore not probative of the step's specific claims and establishes no contradiction.
- [accepted] step 3 [computation] judge: The inference is valid: the stated condition is conjunctive and requires measurements with uncertainty information from at least three independent laboratories covering all four quantities. The previous state explicitly says Collins et al. do not report such three-laboratory measurements and uncertainty budgets, so that study cannot satisfy the condition. No new premise or excluded edge case is introduced.
- [accepted] step 3 sage: The computed conjunction is false under the encoded evidence, which agrees with the step’s claim that Collins et al. do not satisfy the three-laboratory, four-quantity condition.
- [accepted] step 4 [citation] judge: The cited paper exists and supports every added claim: it describes calibration/self-certification procedures, states that illumination and camera-sensor calibration can be performed without a sample, describes stage-to-image calibration, identifies MICAT’s use of a USAF 1951 target for resolution and physical-distance calibration, and states, “This article has no additional data.” The added sentence accurately summarizes these procedures as a workflow and introduces no hidden premise. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf?utm_source=openai))
- [accepted] step 4 extraction: The source spans establish the described self-certification workflow, illumination/camera and stage-to-image calibration, and MICAT use of a USAF 1951 resolution target. They do not verify the separate claim that the article has no additional data, but this lack of support is not a contradiction.
- [FAILED] step 5 [computation] judge: 1. The step assumes Knapper et al. contain no comparative three-laboratory data, but the previous state establishes only that the paper describes a calibration workflow and says there are “no additional data.” A data-accessibility statement of that kind does not imply that no comparative measurements are reported within the article itself.
2. The previous state does not explicitly establish that its summary of Knapper et al. is exhaustive. Listing several calibration procedures does not by itself rule out a three-laboratory dataset elsewhere in the paper.
3. Therefore, although the conditional claim that a workflow without comparative data cannot establish interlaboratory agreement is logically correct, the required antecedent—absence of comparative laboratory data—has not been established in the previous state.
- [accepted] step 5 sage: not grounded: exit code 1: not mechanically recomputable: the step is a qualitative inference from prose about evidentiary sufficiency, not a formal computation derivable from structured data

- [FAILED] step 6 [citation] judge: 1. The catalogue is not represented as exhaustive. Its “Citing publications” section explicitly asks users to notify the project so publications can be added, so absence from this list cannot establish absence of a qualifying peer-reviewed study. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
2. “Current through work listed for 2026” is unsupported and misleading. The page lists two 2026 papers only under “Citing publications,” while the project’s own “Publications and conferences” list ends in 2024; inclusion of some 2026 citations does not demonstrate comprehensive coverage through August 31, 2026. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
3. The catalogue supplies mainly bibliographic entries and titles. It does not document that every listed paper was inspected for measurements from three laboratories, all four quantities, certified targets, and uncertainty budgets. Therefore it cannot by itself justify the detailed content-based negative claim.
4. The page combines journal articles, conference papers, presentations, preprints, and citing publications, including an F1000Research item whose displayed peer-review status includes one approval and one non-approval. Thus the citation does not provide a clean, defined catalogue of exclusively peer-reviewed entries matching the claim’s characterization. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
- [accepted] step 6 extraction: The grounding verifies the page’s description and displayed publication titles, but it does not establish catalogue completeness, currency through 2026, or the absence of the specified interlaboratory study; the 2026 item is unrelated citing work. It therefore does not contradict the step, though it is not probative of the broad absence claim.
- [accepted] step 7 [computation] judge: [PEDANTRY OVERRIDE] The substantive inference is valid: the reviewed sources do not establish the required three-laboratory agreement. “As of August 31, 2026” merely timestamps that evidence review using the applicable current date; it does not materially assert that the catalogue was formally certified complete on that date. Requiring an additional premise for the timestamp is therefore pedantic, especially since the conclusion is expressly limited to “the published evidence reviewed.”
- [accepted] step 7 sage: not grounded: exit code 1: not mechanically recomputable: the conclusion depends on interpreting externally cited publications and a catalogue, not on decidable data contained in the BEFORE state

- [accepted] step 8 [computation] judge: The step correctly converts the established failure of the necessary evidentiary condition into the epistemic conclusion “not demonstrated,” while explicitly avoiding the invalid inference that the laboratories actually disagree. It introduces no new premise beyond the previous state.
- [accepted] step 8 sage: The grounding establishes that if demonstration requires the evidentiary condition and that condition is absent, agreement is not demonstrated, while actual disagreement remains undetermined. This matches the step’s claimed transformation.
TOOL ACTIVITY: citation_judge:web_search x8, convention:web_search x4, formalizer:web_search x9, pedantry:web_search x4, solver:web_search x11, source_namer:web_search x11
STATS: 36 calls, 144.6s

output

{
 "searches": [
  {
   "claim": "Has the proposal's question already been answered: do OpenFlexure microscope measurements of resolution, field curvature, illumination uniformity, and stage repeatability against certified targets agree across three independent labs within stated uncertainties?",
   "queries": [
    "OpenFlexure",
    "\"OpenFlexure microscope\"",
    "\"OpenFlexure microscope\" AND (calibration OR characterization OR metrology)",
    "\"OpenFlexure microscope\" AND (resolution OR \"image quality\") AND (stage OR positioning)",
    "\"OpenFlexure microscope\" AND (\"field curvature\" OR \"field flatness\") AND (\"illumination uniformity\" OR vignetting)",
    "\"OpenFlexure microscope\" AND (interlaboratory OR \"inter laboratory\" OR \"multi site\" OR \"round robin\")",
    "\"OpenFlexure microscope\" AND (reproducibility OR repeatability) AND (laboratory OR lab) AND uncertainty",
    "\"OpenFlexure microscope\" AND (\"USAF 1951\" OR MICAT OR \"certified target\" OR \"reference target\") AND (resolution OR illumination OR stage)",
    "\"OpenFlexure microscope\" AND (interlaboratory OR \"three laboratories\" OR \"three labs\") AND resolution AND \"field curvature\" AND \"illumination uniformity\" AND \"stage repeatability\""
   ],
   "from_date": "",
   "to_date": "2026-08-31",
   "issns": []
  },
  {
   "claim": "Collins et al. do not report measurements and uncertainty budgets from three independent laboratories covering the four specified quantities.",
   "queries": [
    "\"Robotic microscopy for everyone\"",
    "\"Robotic microscopy for everyone\" AND OpenFlexure",
    "\"Robotic microscopy for everyone\" AND (resolution OR calibration OR characterization)",
    "\"Robotic microscopy for everyone\" AND (USAF OR \"resolution target\") AND (uncertainty OR repeatability)",
    "\"Robotic microscopy for everyone\" AND (\"field curvature\" OR vignetting OR \"illumination uniformity\")",
    "\"Robotic microscopy for everyone\" AND (interlaboratory OR \"multiple laboratories\" OR \"three laboratories\")"
   ],
   "from_date": "2019-01-01",
   "to_date": "2021-12-31",
   "issns": []
  },
  {
   "claim": "Knapper et al. do not provide a three-laboratory dataset from which agreement of resolution, field curvature, illumination uniformity, and stage repeatability within stated uncertainties can be established.",
   "queries": [
    "\"Developing the OpenFlexure Microscope towards medical use\"",
    "\"Developing the OpenFlexure Microscope towards medical use\" AND calibration",
    "\"Developing the OpenFlexure Microscope towards medical use\" AND (MICAT OR \"USAF 1951\")",
    "\"Developing the OpenFlexure Microscope towards medical use\" AND (repeatability OR reproducibility OR uncertainty)",
    "\"Developing the OpenFlexure Microscope towards medical use\" AND (interlaboratory OR \"multi site\" OR \"multiple laboratories\")",
    "\"Developing the OpenFlexure Microscope towards medical use\" AND resolution AND \"field curvature\" AND \"illumination uniformity\" AND \"stage repeatability\""
   ],
   "from_date": "2023-01-01",
   "to_date": "2025-12-31",
   "issns": []
  },
  {
   "claim": "No peer-reviewed study reports a three-laboratory OpenFlexure comparison jointly covering resolution, field curvature, illumination uniformity, stage repeatability, certified targets, and uncertainty budgets.",
   "queries": [
    "OpenFlexure AND microscope",
    "OpenFlexure AND (performance OR characterization OR calibration)",
    "OpenFlexure AND (repeatability OR reproducibility OR uncertainty)",
    "OpenFlexure AND (interlaboratory OR \"inter laboratory\" OR \"round robin\" OR \"multi site\")",
    "OpenFlexure AND (\"three laboratories\" OR \"three labs\" OR \"independent laboratories\")",
    "OpenFlexure AND (\"USAF 1951\" OR MICAT OR \"certified target\" OR \"reference standard\") AND uncertainty",
    "OpenFlexure AND resolution AND (\"field curvature\" OR \"field flatness\") AND (\"illumination uniformity\" OR vignetting) AND (\"stage repeatability\" OR \"positioning repeatability\")",
    "OpenFlexure AND interlaboratory AND resolution AND illumination AND stage AND uncertainty"
   ],
   "from_date": "",
   "to_date": "2026-08-31",
   "issns": []
  },
  {
   "claim": "No peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard, and the only reported malaria study is a 2025 Research Square preprint using expert annotation as ground truth.",
   "queries": [
    "OpenFlexure AND diagnosis",
    "OpenFlexure AND diagnostic",
    "OpenFlexure AND malaria",
    "OpenFlexure AND malaria AND (accuracy OR sensitivity OR specificity OR validation)",
    "OpenFlexure AND malaria AND (\"ground truth\" OR annotation OR microscopy)",
    "OpenFlexure AND malaria AND (PCR OR molecular OR \"gold standard\" OR \"reference standard\")",
    "OpenFlexure AND malaria AND \"expert annotation\"",
    "OpenFlexure AND malaria AND \"Research Square\"",
    "OpenFlexure AND malaria AND (preprint OR rs-6809543)"
   ],
   "from_date": "",
   "to_date": "2026-08-31",
   "issns": []
  }
 ]
}

system

You are one role in an automated verified-reasoning pipeline. Your reply is parsed by a program: return exactly what is asked, nothing else. You have no shell or filesystem. Use the web_search tool to verify facts, citations, and definitions rather than relying on recall. Use the code interpreter (Python; sympy/numpy/scipy available) to recompute rather than trusting arithmetic.

You give the screening verdict on one research-proposal question, using the
digest of a verification run: the question (the proposal's hypothesis), the
outcome, the proof, and every audited claim with the checker's full reason.

`verdict` — is the proposal's question genuinely open and worth a human
reviewer's time?
- yes: the run establishes that the question is real, open, and well-posed —
  a certified "not settled by the reviewed evidence", or a checker-verified
  absence of the result the proposal would supply.
- no: the run shows it is not a fundable open question — already settled by
  the literature, ill-posed, or its supporting claims collapse on checkable
  facts.
- maybe: the run leaves specific uncertainties only a human can resolve. If
  openness rests on something the run did not check — whether the analysis
  is already published, whether the data exists — that is maybe, with the
  check as a review item, not yes.

The digest may end with a LITERATURE SEARCH section: engine-run OpenAlex
queries with their total match counts, per claim, broad to narrow; a rung
with at most 10 matches lists them (title, year, venue, doi). Read it as evidence, not as a verdict. Hits whose titles answer the
proposal's question support no (already settled). Zero hits on the narrow
rungs of a calibrated ladder (its broad rungs matched) support yes for that
claim's absence. An uncalibrated ladder establishes nothing, and a FAILED
rung is unknown, not zero. Name the query or hit you rely on.

`explanation`: for yes or no, 2-4 sentences grounded only in the digest.
For maybe, one sentence naming the core uncertainty.

`review_items`: for maybe only — 2 to 6 concrete questions or checks for the
human reviewer, each answerable and each tied to something in the digest.
Empty for yes and no.

user

QUESTION:
For the OpenFlexure microscope, do resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties?

Non-exhaustive sources that may help:
- OpenFlexure Microscope, University of Glasgow; hardware CC-BY-SA-4.0, server software GPLv3; current build v7 (beta) — https://openflexure.org/
- Collins J.T. et al., 'Robotic microscopy for everyone: the OpenFlexure microscope', Biomed Opt Express 11(5):2447 (2020) — https://doi.org/10.1364/BOE.385729
- Knapper J. et al., 'Developing the OpenFlexure Microscope towards medical use', Phil Trans R Soc A 382:20230257 (2024) — https://doi.org/10.1098/rsta.2023.0257
- GAP THIS PROJECT FILLS: no peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard; the only malaria study is a 2025 Research Square preprint with expert annotation as ground truth — https://www.researchsquare.com/article/rs-6809543/v1
- Comparator for a properly powered field validation: Schistoscope, van Lieshout L. et al., PLOS NTD 18(2):e0011967 (2024) -- Sens 62.9-78.0%, Spec 78.8-90.9% vs composite reference — https://doi.org/10.1371/journal.pntd.0011967
- PlanktoScope, Pollina T. et al., Front Mar Sci 9:949428 (2022) -- open modular quantitative imager — https://doi.org/10.3389/fmars.2022.949428
- OSHWA open-hardware certification -- 3,369 certified projects as of Jul 2026 — https://certification.oshwa.org/
- Journal of Open Hardware -- diamond OA since 2023, hosted by Western University Libraries (DOI prefix 10.5206/joh); and HardwareX (Elsevier, gold OA) — https://openhardware.metajnl.com/

OUTCOME: Declined budget_exhausted
DETAIL: step 1 [problem_given] judge: 1. The problem does not state that the measurements must be published; “published” is an added evidentiary premise.
2. The problem says “across three independent labs,” not “at least three independent laboratories.” Treating this as a minimum of three is an interpretation rather than a directly stated value.; step 1 extraction: The engine-witnessed problem statement says only “resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties”; it does not state the added requirement that the measurements be published.; step 5 [computation] judge: 1. The step assumes Knapper et al. contain no comparative three-laboratory data, but the previous state establishes only that the paper describes a calibration workflow and says there are “no additional data.” A data-accessibility statement of that kind does not imply that no comparative measurements are reported within the article itself.
2. The previous state does not explicitly establish that its summary of Knapper et al. is exhaustive. Listing several calibration procedures does not by itself rule out a three-laboratory dataset elsewhere in the paper.
3. Therefore, although the conditional claim that a workflow without comparative data cannot establish interlaboratory agreement is logically correct, the required antecedent—absence of comparative laboratory data—has not been established in the previous state.; step 6 [citation] judge: 1. The catalogue is not represented as exhaustive. Its “Citing publications” section explicitly asks users to notify the project so publications can be added, so absence from this list cannot establish absence of a qualifying peer-reviewed study. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
2. “Current through work listed for 2026” is unsupported and misleading. The page lists two 2026 papers only under “Citing publications,” while the project’s own “Publications and conferences” list ends in 2024; inclusion of some 2026 citations does not demonstrate comprehensive coverage through August 31, 2026. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
3. The catalogue supplies mainly bibliographic entries and titles. It does not document that every listed paper was inspected for measurements from three laboratories, all four quantities, certified targets, and uncertainty budgets. Therefore it cannot by itself justify the detailed content-based negative claim.
4. The page combines journal articles, conference papers, presentations, preprints, and citing publications, including an F1000Research item whose displayed peer-review status includes one approval and one non-approval. Thus the citation does not provide a clean, defined catalogue of exclusively peer-reviewed entries matching the claim’s characterization. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications)) [budget exhausted: formalizer]
PROOF (final round):
State 0: ['ANSWER']
State 1: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.']  [problem_given] This is the conjunctive evidentiary requirement stated in the question.
State 2: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.']  [citation] Collins et al., section 2.2, reports the target, 480 nm central-field result, qualitative edge degradation, and computational vignetting correction; its reported experiment is not a three-laboratory comparison. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
State 3: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.']  [computation] The cited study lacks the required interlaboratory measurements and uncertainty comparison, so the conjunctive condition is not met by that study.
State 4: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.']  [citation] The calibration section describes these procedures and the data-accessibility statement says the article has no additional data. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf))
State 5: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.']  [computation] A proposed calibration workflow without comparative laboratory data cannot establish interlaboratory agreement.
State 6: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets."]  [citation] Inspection of the project's catalogue of peer-reviewed outputs and citing publications shows application, calibration, autofocus, optical-mode, and stage papers, but no listed three-site interlaboratory metrology study of the specified form. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications?utm_source=openai))
State 7: ['ANSWER', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Neither principal characterization source supplies the required comparison, and the current publication catalogue identifies no qualifying interlaboratory study.
State 8: ['ANSWER = No. Agreement across three independent laboratories within stated uncertainties has not been demonstrated; this is absence of establishing evidence, not evidence that the laboratories disagree.', 'A positive answer requires published measurements from at least three independent laboratories covering all four specified quantities—resolution, field curvature, illumination uniformity, and stage repeatability—against certified targets, with stated uncertainties permitting an agreement assessment.', 'Collins et al. report a 480 nm point-spread-function FWHM over the central 50% of the field using an edge on a USAF target; they describe reduced edge resolution from field curvature and aberration and correction of sensor vignetting through a lens-shading table, but do not report measurements and uncertainty budgets from three independent laboratories.', 'Therefore, Collins et al. do not satisfy the required three-laboratory, four-quantity agreement condition.', 'Knapper et al. describe calibration and proposed self-certification: illumination and camera calibration, stage-to-image calibration, and MICAT resolution calibration using a USAF 1951 target; they present this as a workflow and state that the article has no additional data.', 'Therefore, Knapper et al. do not provide a three-laboratory dataset from which agreement of the four quantities within stated uncertainties can be established.', "The OpenFlexure project's publication catalogue, current through work listed for 2026, contains no peer-reviewed entry reporting a three-laboratory comparison jointly covering the four specified metrological quantities and their uncertainty budgets.", 'Thus, as of August 31, 2026, the published evidence reviewed does not meet the necessary condition for establishing the claimed interlaboratory agreement.']  [computation] Failure of the necessary evidentiary condition resolves the answer as “not demonstrated”; logically, lack of such evidence does not establish actual disagreement.
AUDITED CLAIMS:
- [accepted] state 0: State 0 contains only “ANSWER,” which is an allowed goal placeholder, and it contains no added premises, conclusions, computations, or other unsupported content.
- [FAILED] step 1 [problem_given] judge: 1. The problem does not state that the measurements must be published; “published” is an added evidentiary premise.
2. The problem says “across three independent labs,” not “at least three independent laboratories.” Treating this as a minimum of three is an interpretation rather than a directly stated value.
- [FAILED] step 1 extraction: The engine-witnessed problem statement says only “resolution, field curvature, illumination uniformity and stage repeatability measured against certified targets agree across three independent labs within the stated uncertainties”; it does not state the added requirement that the measurements be published.
- [accepted] step 2 [citation] judge: The cited paper supports every added claim: section 2.2 derives a 480 nm PSF FWHM from an edge on a USAF resolution target, describes near-diffraction-limited performance over the central 50% of the field and decreased edge resolution caused by field curvature and aberration, and describes vignetting correction by overriding the lens-shading table. The paper contains no three-independent-laboratory comparison or associated uncertainty budgets. No hidden premise is introduced. ([api.repository.cam.ac.uk](https://api.repository.cam.ac.uk/server/api/core/bitstreams/b59c5291-de52-4f84-a84c-435d38f75c94/content))
- [accepted] step 2 extraction: The extracted passages discuss chromatic-aberration mitigation and qualitative parasite resolving performance, but do not address the claimed USAF-target measurement, 480 nm FWHM, central-field coverage, field curvature, vignetting correction, uncertainty budgets, or laboratory count. The grounding is therefore not probative of the step's specific claims and establishes no contradiction.
- [accepted] step 3 [computation] judge: The inference is valid: the stated condition is conjunctive and requires measurements with uncertainty information from at least three independent laboratories covering all four quantities. The previous state explicitly says Collins et al. do not report such three-laboratory measurements and uncertainty budgets, so that study cannot satisfy the condition. No new premise or excluded edge case is introduced.
- [accepted] step 3 sage: The computed conjunction is false under the encoded evidence, which agrees with the step’s claim that Collins et al. do not satisfy the three-laboratory, four-quantity condition.
- [accepted] step 4 [citation] judge: The cited paper exists and supports every added claim: it describes calibration/self-certification procedures, states that illumination and camera-sensor calibration can be performed without a sample, describes stage-to-image calibration, identifies MICAT’s use of a USAF 1951 target for resolution and physical-distance calibration, and states, “This article has no additional data.” The added sentence accurately summarizes these procedures as a workflow and introduces no hidden premise. ([eprints.gla.ac.uk](https://eprints.gla.ac.uk/327438/2/327438.pdf?utm_source=openai))
- [accepted] step 4 extraction: The source spans establish the described self-certification workflow, illumination/camera and stage-to-image calibration, and MICAT use of a USAF 1951 resolution target. They do not verify the separate claim that the article has no additional data, but this lack of support is not a contradiction.
- [FAILED] step 5 [computation] judge: 1. The step assumes Knapper et al. contain no comparative three-laboratory data, but the previous state establishes only that the paper describes a calibration workflow and says there are “no additional data.” A data-accessibility statement of that kind does not imply that no comparative measurements are reported within the article itself.
2. The previous state does not explicitly establish that its summary of Knapper et al. is exhaustive. Listing several calibration procedures does not by itself rule out a three-laboratory dataset elsewhere in the paper.
3. Therefore, although the conditional claim that a workflow without comparative data cannot establish interlaboratory agreement is logically correct, the required antecedent—absence of comparative laboratory data—has not been established in the previous state.
- [accepted] step 5 sage: not grounded: exit code 1: not mechanically recomputable: the step is a qualitative inference from prose about evidentiary sufficiency, not a formal computation derivable from structured data

- [FAILED] step 6 [citation] judge: 1. The catalogue is not represented as exhaustive. Its “Citing publications” section explicitly asks users to notify the project so publications can be added, so absence from this list cannot establish absence of a qualifying peer-reviewed study. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
2. “Current through work listed for 2026” is unsupported and misleading. The page lists two 2026 papers only under “Citing publications,” while the project’s own “Publications and conferences” list ends in 2024; inclusion of some 2026 citations does not demonstrate comprehensive coverage through August 31, 2026. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
3. The catalogue supplies mainly bibliographic entries and titles. It does not document that every listed paper was inspected for measurements from three laboratories, all four quantities, certified targets, and uncertainty budgets. Therefore it cannot by itself justify the detailed content-based negative claim.
4. The page combines journal articles, conference papers, presentations, preprints, and citing publications, including an F1000Research item whose displayed peer-review status includes one approval and one non-approval. Thus the citation does not provide a clean, defined catalogue of exclusively peer-reviewed entries matching the claim’s characterization. ([openflexure.gitlab.io](https://openflexure.gitlab.io/about/publications))
- [accepted] step 6 extraction: The grounding verifies the page’s description and displayed publication titles, but it does not establish catalogue completeness, currency through 2026, or the absence of the specified interlaboratory study; the 2026 item is unrelated citing work. It therefore does not contradict the step, though it is not probative of the broad absence claim.
- [accepted] step 7 [computation] judge: [PEDANTRY OVERRIDE] The substantive inference is valid: the reviewed sources do not establish the required three-laboratory agreement. “As of August 31, 2026” merely timestamps that evidence review using the applicable current date; it does not materially assert that the catalogue was formally certified complete on that date. Requiring an additional premise for the timestamp is therefore pedantic, especially since the conclusion is expressly limited to “the published evidence reviewed.”
- [accepted] step 7 sage: not grounded: exit code 1: not mechanically recomputable: the conclusion depends on interpreting externally cited publications and a catalogue, not on decidable data contained in the BEFORE state

- [accepted] step 8 [computation] judge: The step correctly converts the established failure of the necessary evidentiary condition into the epistemic conclusion “not demonstrated,” while explicitly avoiding the invalid inference that the laboratories actually disagree. It introduces no new premise beyond the previous state.
- [accepted] step 8 sage: The grounding establishes that if demonstration requires the evidentiary condition and that condition is absent, agreement is not demonstrated, while actual disagreement remains undetermined. This matches the step’s claimed transformation.
TOOL ACTIVITY: citation_judge:web_search x8, convention:web_search x4, formalizer:web_search x9, pedantry:web_search x4, solver:web_search x11, source_namer:web_search x11
LITERATURE SEARCH (engine-witnessed, openalex, as of 2026-09-02; total matches per query, queries broad -> narrow):
- CLAIM: Has the proposal's question already been answered: do OpenFlexure microscope measurements of resolution, field curvature, illumination uniformity, and stage repeatability against certified targets agree across three independent labs within stated uncertainties?  [UNCALIBRATED: no query matched anything, so this says nothing about absence]
    FAILED hits: OpenFlexure
    FAILED hits: "OpenFlexure microscope"
    FAILED hits: "OpenFlexure microscope" AND (calibration OR characterization OR metrology)
    FAILED hits: "OpenFlexure microscope" AND (resolution OR "image quality") AND (stage OR positioning)
    FAILED hits: "OpenFlexure microscope" AND ("field curvature" OR "field flatness") AND ("illumination uniformity" OR vignetting)
    FAILED hits: "OpenFlexure microscope" AND (interlaboratory OR "inter laboratory" OR "multi site" OR "round robin")
    FAILED hits: "OpenFlexure microscope" AND (reproducibility OR repeatability) AND (laboratory OR lab) AND uncertainty
    FAILED hits: "OpenFlexure microscope" AND ("USAF 1951" OR MICAT OR "certified target" OR "reference target") AND (resolution OR illumination OR stage)
    FAILED hits: "OpenFlexure microscope" AND (interlaboratory OR "three laboratories" OR "three labs") AND resolution AND "field curvature" AND "illumination uniformity" AND "stage repeatability"
- CLAIM: Collins et al. do not report measurements and uncertainty budgets from three independent laboratories covering the four specified quantities.  [UNCALIBRATED: no query matched anything, so this says nothing about absence]
    FAILED hits: "Robotic microscopy for everyone"
    FAILED hits: "Robotic microscopy for everyone" AND OpenFlexure
    FAILED hits: "Robotic microscopy for everyone" AND (resolution OR calibration OR characterization)
    FAILED hits: "Robotic microscopy for everyone" AND (USAF OR "resolution target") AND (uncertainty OR repeatability)
    FAILED hits: "Robotic microscopy for everyone" AND ("field curvature" OR vignetting OR "illumination uniformity")
    FAILED hits: "Robotic microscopy for everyone" AND (interlaboratory OR "multiple laboratories" OR "three laboratories")
- CLAIM: Knapper et al. do not provide a three-laboratory dataset from which agreement of resolution, field curvature, illumination uniformity, and stage repeatability within stated uncertainties can be established.  [UNCALIBRATED: no query matched anything, so this says nothing about absence]
    FAILED hits: "Developing the OpenFlexure Microscope towards medical use"
    FAILED hits: "Developing the OpenFlexure Microscope towards medical use" AND calibration
    FAILED hits: "Developing the OpenFlexure Microscope towards medical use" AND (MICAT OR "USAF 1951")
    FAILED hits: "Developing the OpenFlexure Microscope towards medical use" AND (repeatability OR reproducibility OR uncertainty)
    FAILED hits: "Developing the OpenFlexure Microscope towards medical use" AND (interlaboratory OR "multi site" OR "multiple laboratories")
    FAILED hits: "Developing the OpenFlexure Microscope towards medical use" AND resolution AND "field curvature" AND "illumination uniformity" AND "stage repeatability"
- CLAIM: No peer-reviewed study reports a three-laboratory OpenFlexure comparison jointly covering resolution, field curvature, illumination uniformity, stage repeatability, certified targets, and uncertainty budgets.  [UNCALIBRATED: no query matched anything, so this says nothing about absence]
    FAILED hits: OpenFlexure AND microscope
    FAILED hits: OpenFlexure AND (performance OR characterization OR calibration)
    FAILED hits: OpenFlexure AND (repeatability OR reproducibility OR uncertainty)
    FAILED hits: OpenFlexure AND (interlaboratory OR "inter laboratory" OR "round robin" OR "multi site")
    FAILED hits: OpenFlexure AND ("three laboratories" OR "three labs" OR "independent laboratories")
    FAILED hits: OpenFlexure AND ("USAF 1951" OR MICAT OR "certified target" OR "reference standard") AND uncertainty
    FAILED hits: OpenFlexure AND resolution AND ("field curvature" OR "field flatness") AND ("illumination uniformity" OR vignetting) AND ("stage repeatability" OR "positioning repeatability")
    FAILED hits: OpenFlexure AND interlaboratory AND resolution AND illumination AND stage AND uncertainty
- CLAIM: No peer-reviewed study reports OpenFlexure diagnostic accuracy against a molecular gold standard, and the only reported malaria study is a 2025 Research Square preprint using expert annotation as ground truth.  [UNCALIBRATED: no query matched anything, so this says nothing about absence]
    FAILED hits: OpenFlexure AND diagnosis
    FAILED hits: OpenFlexure AND diagnostic
    FAILED hits: OpenFlexure AND malaria
    FAILED hits: OpenFlexure AND malaria AND (accuracy OR sensitivity OR specificity OR validation)
    FAILED hits: OpenFlexure AND malaria AND ("ground truth" OR annotation OR microscopy)
    FAILED hits: OpenFlexure AND malaria AND (PCR OR molecular OR "gold standard" OR "reference standard")
    FAILED hits: OpenFlexure AND malaria AND "expert annotation"
    FAILED hits: OpenFlexure AND malaria AND "Research Square"
    FAILED hits: OpenFlexure AND malaria AND (preprint OR rs-6809543)
STATS: 36 calls, 144.6s

reasoning

{
 "summary": [
  "**Evaluating output needs**\n\nI need to ensure the output is in exact JSON format. The verdict might rely on whether there's thorough literature and data available. There’s a core uncertainty about the issue. I should review items 2-6 and create a grounded summary. I need to differentiate the questions, perhaps by proposing an experiment that checks if the measurements are genuinely open. It seems the budget is exhausted, leading to unsuccessful claims. A concise explanation will help clarify concrete items."
 ]
}

output

{
 "verdict": "maybe",
 "explanation": "The core uncertainty is whether any existing study or dataset already contains the specified three-lab, four-metric comparison, because the run did not exhaustively inspect Knapper et al. or the literature and every OpenAlex search rung failed rather than returning calibrated zero results.",
 "review_items": [
  "Inspect the full Knapper et al. article and supplements for comparative measurements from exactly three independent laboratories covering all four specified quantities and their uncertainties.",
  "Run a calibrated literature search whose broad OpenFlexure queries return known papers, then determine whether narrow interlaboratory-metrology queries produce zero qualifying studies.",
  "Search beyond the non-exhaustive OpenFlexure publication catalogue, including bibliographic databases, repositories, preprints, conference proceedings, and project data archives.",
  "Determine whether unpublished measurements or accessible datasets already exist from three independent labs using certified targets and documented uncertainty budgets.",
  "Clarify whether the proposal concerns exactly three laboratories and whether peer-reviewed publication is required, neither of which was established by the question."
 ]
}