An AI-assisted manuscript claims that for a compact connected Lie group G, the kernel of Haar integration is a Mathieu–Zhao space exactly when G is a torus. Its public record is author-side only: an author-checked manuscript plus an author-run SymPy identity verifier. We re-verified the manuscript’s computational supporting identities independently — our own BigInt-rational multivariate Laurent-polynomial arithmetic (including ℚ[i] for the square-root-free substitution), written without executing the author’s script. All 126 checks hold exactly; 3/3 planted mutations are rejected.
node verify.js · exit 0 · 0.04 s · no dependenciesWith the manuscript’s conventions (Laurent constant term CTw; Haar moment 2∫₀¹CTw(·)·x dx; cm = ∫₀¹(1−t²)mdt): the weighted xz(1,1) witness moments m = 1…6; the abelian pair U, V, T, P with its printed expansion, w-spectrum {−1,0,1,2} and the relations U·V + T² − 1 = 0 and U·P; torus-scaling invariance of all six matrix-entry representatives and the square-root-free B(x,w) reparametrization; the Pascal-row moment identity 2∫CTw(QsPm)x dx = cm·C(m−1,s−1) for m ≤ 5, all admissible s; the reduced Hopf coefficient identity through m = 8; and the closed form cm = 4m(m!)²/(2m+1)!. Mutations — a perturbed coefficient, a sign flip in T, a wrong Pascal row — are all caught.
The theorem. The verifier — the author’s and ours alike — checks finite supporting identities, not the classification. The general-m extension of every spot check, the representation-theoretic transfer (orbit averaging, highest-weight construction, central-quotient descent, adjoint pullback), the reduction of Haar integration to a constant term, and positivity outside the checked ranges are all unaudited mathematics. The formulation. Our implementation and the author’s share the manuscript’s definitions; an error identical in both would pass — the same transcription-gate caveat as pilot #1.
Part of the independent-verification lane — this page is unit 2 of six. Pilot #1 (the rank-two Poisson counterexample) and pilot #2 are the two “bankers”: fast, fully exact, decisive on their computational layer. The flagship (the Korenblum constant, re-derived in our own outward-rounded interval arithmetic) went green alongside them on 2026-08-03, and three further units on 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, 126 exact checks, 3/3 planted
mutations rejected.