Carlos Toledo
Research note — not peer-reviewed. Each verifier below has been shown to fail on a deliberately broken copy of itself and pass on the real one. No contact with any claim’s author or with the claim database has been made — that, like every send, is an owner action.
Independent verification · challenges · 2026-08-03 · extended 2026-08-04

We re-checked six AI-claimed results in our own arithmetic. Five hold; the sixth holds on every fragment a machine can check.

Roughly 400 AI-assisted mathematical results sit in a public claim database. On every numeric one we examined, the verification label is the author’s own — the author’s manuscript, the author’s script, the author’s run. We picked six, from the weakest prior evidence to the strongest, and rebuilt each check from scratch: our own arithmetic, no shared code, a planted bug in every verifier to prove the check can fail. Five are CONFIRMED on the layer we checked; one is PARTIAL — its machine-checkable fragment confirmed in full, its analytic core not audited. Total runtime: under five seconds.

ClaimVerdictWhat existed beforeWhat we ranTime
Rank-two Poisson counterexample CONFIRMED (computational claims) author-checked manuscript + author-run scripts our own exact rationals in ℚ[x,q,p,z]0.4 s
Mathieu–Zhao classification identities CONFIRMED (identities only) author-checked manuscript + author-run SymPy our own BigInt Laurent polynomials, incl. ℚ[i]0.04 s
Korenblum constant c₂ ≥ 0.4263 CONFIRMED (numerical side) a published, rigorous Arb certificate our own outward-rounded intervals, no Arb4.2 s
Ran–Teng Conjecture 20 spectral region PARTIAL — fragment CONFIRMED, analytic core not audited human-checked proof, no code, no certificate exact polynomial identities + certified eigenvalue enclosures (272 matrices)41 ms
Erdős #1038 extremal constant D (30 decimals) CONFIRMED (computational fragment) author-checked manuscript + author-run Arb/SymPy certificates our own two-backend intervals + AD + Krawczyk, 45-digit enclosure< 0.1 s
Maxwell 1873 refutation: 24 critical points, 5 charges CONFIRMED at ε = 1/6 (one pinned instance) author-run Mathematica/Maple float checks, no artifact 24 disjoint Krawczyk boxes + interval Hessian nondegeneracy0.1 s

What a confirmation is worth

We went looking for errors in AI-claimed mathematics and found no mathematical error. On the layers we checked, five claims are confirmed outright and the sixth — Ran–Teng — is confirmed on every fragment a machine can check, with its analytic core left explicitly unaudited: a PARTIAL we state as PARTIAL rather than smooth away. The sharpest thing the lane surfaced is fine print, not refutation: the Erdős #1038 manuscript’s headline constant carries a rounded 30th decimal presented with an expansion’s trailing ellipsis, and one of its face inequalities is uncertifiable by naive interval evaluation at the printed radii — both caught only because an independent implementation produced its own certified expansion. What we found beyond that is that nobody had looked — including at the ones that already ship rigorous certificates, where our margins matched theirs from implementations that share no code with them.

That is the more useful result. A refutation would have been a fact about one paper; a confirmation from an independent implementation is a fact about the infrastructure — it says the checking layer can be reconstructed by a stranger, cheaply, and that doing so is currently nobody’s job. It is also the discipline this shop holds itself to elsewhere: a verification lane that only publishes its refutations is a lane you cannot trust.

What none of the six establishes

Each page states, in the same place and the same words, exactly what it did not check — and on all six, the theorem sitting above the checked layer is still nobody’s job. We confirm computational layers: bracket relations and a Jacobian, a family of moment identities, a finite system of inequalities, the algebra and certified enclosures of a spectral-region proof, the implicit definition and digits of an extremal constant, one pinned instance of a counterexample configuration. We do not audit the Poisson conjecture’s disproof logic, the Mathieu–Zhao classification theorem, Korenblum’s duality argument, Ran–Teng’s analytic necessity argument, the Erdős #1038 extremality proof, or Maxwell-refutation Theorem 1’s asymptotic statement. And in every case our implementation and the author’s share the manuscript’s formulation: an error identical in both would pass.

research/challenges · six verifiers, each node verify.js, no dependencies · claim source: aimath.robertj1.com · first three green 2026-08-03 · ranteng / lemniscate / maxwell green 2026-08-04