Independent scrutiny of published mathematical and theoretical claims.
What was claimed. What was tested. What survived.
As Stated examines published theoretical claims one at a time: theorems, lemmas, propositions, algorithms and constructions in game theory, mechanism design, and matching and social choice. Each record gives the exact claim, what was tested, what was found, how the finding was verified and what it does not establish.
Recent case records
All 3 papers and 5 claimsEach paper is listed with every claim that was investigated in it. A paper can contain a claim that survived and another that did not, so there is no verdict on the paper as a whole.
| Claim | Finding | Verification | Development |
|---|---|---|---|
Safe implementationMalachy J. Gavan and Antonio Penta · Theoretical Economics 20(4) (2025), 1285–1322 1 claim · updated 7 November 2026 | |||
| Theorem 3 proof constructionConstruction · main resultThe four-rule message mechanism displayed in the proof implements the correspondence throughout the stated domain. | Construction failsThe displayed mechanism can select an outcome outside F at a pure Nash equilibrium. | AIPrivate humanfull source check | — |
A Qualitative Theory of Large Games with Strategic ComplementaritiesŁukasz Balbus, Paweł Dziewulski, Kevin Reffett and Łukasz Woźny · Economic Theory 67 (2019), 497–523 2 claims · updated 7 November 2026 | |||
| Theorem 1(i)Theorem · main resultUnder Assumption 1, greatest and least distributional equilibria exist. | False as statedThe literal one-way order condition admits a game satisfying Assumption 1 with no distributional equilibrium. | AIPrivate humanpartial source check | — |
| Lemma A1 proof: function-space stepLemma · auxiliary resultThe proof treats M(X)-M(X), where M(X) contains bounded measurable isotone functions, as a Riesz subspace of C(X). | Missing assumptionMeasurability and isotonicity do not imply continuity, so the asserted inclusion in C(X) does not follow. | AIPrivate humanpartial source check | — |
Stability and strategy-proofness for matching with constraints: A necessary and sufficient conditionYuichiro Kamada and Fuhito Kojima · Theoretical Economics 13 (2018), 761–793 2 claims · updated 6 November 2026 | |||
| Theorem 1Theorem · main resultA hierarchical region family admits a stable, doctor-strategy-proof mechanism. | No defect foundNo counterexample or nontrivial proof gap survived the recorded audit of the hierarchy direction. | Deep auditfull source check | — |
| Theorem 2Theorem · main resultFor a non-hierarchical region family, no stable, doctor-strategy-proof mechanism works across the full admitted domain. | No defect foundNo counterexample or nontrivial proof gap survived the recorded audit of the non-hierarchy impossibility direction. | Deep auditfull source check | — |
Reading a finding
- 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.
How a claim is examined
- 1State the claim exactly
Every definition, assumption and quantifier is taken from the published version.
- 2Try to break it
Search for counterexamples and for steps in the proof that fail.
- 3Try to rescue it
Look for the intended reading and for a repair before reporting a problem.
- 4Confirm
A defect counts only after two different kinds of check, at least one of them by a human.