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.
node verify.js · exit 0 · 0.4 s · no dependenciesWith the manuscript’s canonical bracket {f,g} = fpgx − fxgp + fzgq − fqgz 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.
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.
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. Part of the independent-verification lane — this page is unit 1 of six. All six shipped by 2026-08-04; the collective verdict — five CONFIRMED, one PARTIAL, under five seconds of total runtime — and the list of what none of the six establishes are on the lane index.
The program is published beside this page:
verify.js — plain
Node, no dependencies, node verify.js, exit 0, both planted mutations
rejected.