Exactly the tori — a classification. For which compact connected Lie groups G is the kernel of Haar integration on R(G) a Mathieu–Zhao space?
| field | as recorded at source |
|---|---|
| the claim | Exactly the tori — a classification. |
| the problem | For which compact connected Lie groups G is the kernel of Haar integration on R(G) a Mathieu–Zhao space? |
| credited AI system | not recorded at source |
| verification at source | An author SymPy script, which we read but did not execute. |
| our verdict | CONFIRMED supporting identities only |
Every supporting identity the classification rests on, exactly over ℚ with BigInt rational Laurent arithmetic: the weighted witness moments, the explicit abelian pair and its printed four-term expansion, the matrix-entry representatives and their invariance. Disclosure specific to this lane: the author’s Python was READ to cross-check which identities the TeX intended — its blocks match the manuscript and are the ones re-verified here — but it was never executed, and no value on this page came from it.
This verifier reports a summary rather than named rows. It states its own totals and its mutation-control outcome and stops there, so there is no per-check ledger to show and this page does not manufacture one. Its complete output at this build is reproduced verbatim:
checks: 126, failures: 0, mutation controls rejected: 3/3, runtime: 0.04s ALL SUPPORTING IDENTITIES VERIFIED EXACTLY (BigInt rationals).
A verifier that cannot reject a false claim is not evidence, it is decoration. So each one carries mutation controls: the claim is deliberately corrupted and the verifier must refuse it. All 3 were rejected in the run that built this page, and a control that stopped firing would refuse the page instead.
This verifier reports 3 controls rejected as a count rather than naming them individually, so there is nothing to list here beyond that count. The count is parsed from its output, not asserted.
The classification theorem itself. Confirming the identities a proof uses is not confirming the proof, and this lane is the clearest case of that distinction in the set.
This is the part worth reading twice. The verdict at the top of this page is true inside its scope line and false outside it, and the sentence above is where the scope line comes from. Across all six claims in this set the same split appears: the computational fragment certifies and the analytic core does not — the flagship page measures exactly that.
git clone https://github.com/carlostoledo1891/cert-machine cd cert-machine node legacy/research/challenges/lane/laneb-mathieu/verify.js
Plain Node, no packages. It prints the ledger above, runs its own falsifiers, and exits non-zero if anything fails. node instruments/laneaudit/audit.js runs all six.