Methodology

The question

Does a published theoretical claim follow from the assumptions stated with it? The claim may be a theorem, proposition, lemma, corollary, remark, algorithm, construction or application, in game theory, mechanism design, matching and social choice, or related fields. The unit of investigation is the single claim, read exactly as stated. A paper is not given a verdict as a whole.

Process

1. Select. Papers are chosen deliberately. Many are screened from their metadata; fewer are investigated claim by claim.
2. State the claim exactly. Every definition, assumption and quantifier is taken from the published version.
3. Try to break it. Search for counterexamples and for steps in the proof that fail.
4. Try to rescue it. Look for the intended reading and for a repair before reporting a problem.
5. Confirm. A defect counts only after two different kinds of check, at least one of them by a human.
6. Author contact. Contact is optional. Substantive responses already available are considered, while private correspondence stays private.
7. Release and maintain. Each real release has an exact SHA-256 manifest. Responses, corrections and our own errors become new, dated versions.

Confirmation standard

A suspected defect is confirmed only after at least two confirming checks of different kinds, at least one of them by a human, and with no refuting check left unaddressed. Rerunning the original evidence package does not count as a check.

Only confirmed defects are published as defects. Candidates supported only by AI rechecks are counted in the statistics as open, not named.

Findings

Each investigated claim receives one of six findings.

• No defect foundA deep audit within a stated scope found no defect. This is not a proof that the claim is correct.
• False as statedThe claim, read exactly as printed with its stated assumptions, is false. A counterexample is given.
• Proof incompleteThe proof does not establish the claim as written. The claim itself is not shown to be false, and a repair may exist.
• Missing assumptionThe claim holds only under an assumption that the paper does not state.
• Construction failsA mechanism, algorithm or other construction does not do what the paper says it does.
• UnresolvedThe question could not be settled, usually because the relevant version of the source could not be obtained. Not counted as a defect.

Verification

Each confirmed defect lists the kinds of check that confirmed it: a separate AI recheck, a reproduction by the researcher, an external human verification, and written agreement by the authors. The case index shows the AI recheck as a small dashed "AI" tag, set apart from three squares for the human checks, because AI agreement is not independent human confirmation. Each record also states how far the finding was checked against the published version of the paper.

Negative audits

A negative audit reports an unsuccessful attempt to find a defect within a stated scope. It is not a proof that the result is correct. Each negative audit states what was tested and its limits. Only deep audits are published by name; lighter screens appear only in counts.

Source check

Findings are checked against the version of record. Each claim states whether every decisive element was checked on rendered pages of the published version (full), only partly (partial), or whether the needed version could not be obtained. A question that depends on an unobtainable version is reported as unresolved, not as a defect. It is shown only inside a record released for other, settled claims in the same paper, and the record is revised if the missing version becomes available.

Author contact

Author notification, a waiting period and author consent are not publication gates. The researcher may contact authors as part of the research process, especially when a possible defect is found, and any substantive response already available is considered when preparing the record. Private correspondence remains private unless separately approved for public use. A concrete journal, correction or collaboration strategy may still justify a case-specific hold.

How AI is used

AI models search for counterexamples, write test code and recheck results in separate sessions. They do not decide what is published. Every published defect has also been checked by a human, and the researcher makes every editorial decision. Each record states how AI was used in that case.

Author responses

• Author contact is optional and is not required before or after publication.
• If a substantive written response already exists, it is considered in the record and may motivate further checking.
• An author's disagreement is evidence to assess, not a veto over publication.
• A reply is published only as the authors' own public statement, wording they separately approve for public use, or a link to their public statement.
• Private correspondence is never quoted or summarized publicly without separate consent.

When public author-response information exists, it is recorded in the history of the case it concerns.

Corrections and withdrawals

• Released versions are never edited. Every change is a new version with a dated change note; earlier versions stay online.
• Our own errors are labelled as our corrections. If a finding changes, older versions point to the current one.
• A finding we no longer stand behind is withdrawn: the record stays online with the reason.
• A published correction by the authors or journal is added to the record, and described as crediting this audit only if it says so.
• Material published by mistake is removed, and a short notice records the removal without repeating the content.

Challenges and replications

Anyone may challenge or replicate a published record. Substantive challenges are checked and their outcome is added to the record; replications are credited by name with consent. Allegations about papers not on this site should not be sent through public channels.

Selection and statistics

Papers are chosen deliberately, not sampled at random. These counts describe this programme's work and cannot be read as error rates in published research. Statistics are counts with stated units; small counts that could identify an unpublished case are suppressed.

How releases are approved

Every real record version has a release manifest containing the SHA-256 of its exact public data file. The site build refuses a missing or mismatched manifest. Public versions are immutable: corrections use a new version. The owner approves each release. Automated tests and a privacy scan must pass before it deploys.

Real releases use exact SHA-256 manifests.

What we do not do

• Publish anonymous or unchecked allegations.
• Rank journals, fields or authors.
• Report error rates for published research.
• Name a paper because a candidate was rejected or remains unresolved.