Research note — not peer-reviewed. Pilot #1 of the independent-verification lane: an AI-claimed mathematical result, re-verified in our own arithmetic with checks proven able to fail. No contact with the claim's author or the database maintainer has been made — that, like every send, is an owner action.

Lane B pilot · AI-claimed results · challenges · 2026-08-03

The rank-two Poisson counterexample holds — in arithmetic that shares no code with the author’s

A recent AI-assisted manuscript claims explicit polynomials R, T, D, S ∈ ℚ[x,q,p,z] forming a Poisson endomorphism with Jacobian determinant one and a three-point fiber. The public record is author-side only: an author-checked manuscript and four author-run audits. We re-verified the computational claims independently — our own sparse-polynomial arithmetic over exact BigInt rationals, written without executing the author’s scripts. Every claimed identity holds exactly, and both planted mutations are rejected.

Verdict · node verify.js · exit 0 · 0.4 s · no dependencies

Verdict

CONFIRMED (computational claims)

Bracket relations

{D,R}=1 · {S,T}=1 · 4 cross-brackets ≡ 0

Jacobian

det J(R,T,D,S) ≡ 1, symbolic

Fiber membership

3 points → (0, 1/8, 0, 0), exact

Mutation controls

2 / 2 rejected

Source pinned

commit 85cd90f

Independence, stated precisely: polynomials were extracted from the TeX manuscript and cross-checked against one author verifier by reading, not running; the arithmetic, the bracket implementation, and the determinant expansion are ours. What survives is agreement between two implementations built from the same formulation — stronger than an author-only record, weaker than a second derivation of the formulation itself.

What was verified

With the manuscript’s canonical bracket {f,g} = f_pg_x − f_xg_p + f_zg_q − f_qg_z on the pairs (x,p), (q,z): the canonical-pair relations {D,R} = 1 and {S,T} = 1; the vanishing of all four cross-brackets, identically as polynomials; the 4×4 symbolic Jacobian determinant equal to 1; and exact substitution of the three claimed fiber points (0, 0, 1/24, −1/8) and (±1, ±2/3, 247/96, −89/64), each mapping to (0, 1/8, 0, 0). Two mutation controls give the check its teeth: perturbing one coefficient of R fails three checks; swapping the bracket sign fails two.

What was not verified, stated so it cannot be assumed

Fiber exhaustiveness — we verified the three points lie in the fiber, not that the fiber is exactly three points. The conjecture-level interpretation — that these identities constitute a disproof in the intended sense (the manuscript’s argument that a Poisson endomorphism with a noninjective point map is not an automorphism, and the Jacobian/Dixmier reduction chain) is mathematics we did not audit. The formulation itself — both our verifier and the author’s share the manuscript’s definitions; an error identical in TeX and in both implementations would pass. This is the same transcription-gate honesty the house applies to its own cross-language checks.

Why this lane exists

The claim database records ~404 AI-assisted results; none of the numeric ones we examined carries third-party verification — every label is author-side. A verification lane that is independent, exact, mutation-tested, and fast (this one: 0.4 s) is the missing infrastructure, and this pilot is its first datapoint. Next pilots, in order: the compact Lie-group identity verifier (banker #2), then the Korenblum constant’s Arb certificate re-derived in our own outward-rounded interval arithmetic (flagship).

research/challenges/laneb-poisson · verify.js — own implementation, exact BigInt rationals · VERDICT.md — full record incl. sources at commit 85cd90f · claim source: aimath.robertj1.com; artifacts: github.com/octonion/mathematics/poisson · battery green 2026-08-03