An explicit counterexample: polynomials R, T, D, S in ℚ[x,q,p,z] with prescribed bracket relations. A conjecture about rank-two Poisson structures.
| field | as recorded at source |
|---|---|
| the claim | An explicit counterexample: polynomials R, T, D, S in ℚ[x,q,p,z] with prescribed bracket relations. |
| the problem | A conjecture about rank-two Poisson structures. |
| credited AI system | not recorded at source |
| verification at source | The author’s own scripts, which we neither derived from nor executed. |
| our verdict | CONFIRMED the explicit counterexample |
All six bracket relations ({D,R} = 1, {S,T} = 1 and the four vanishing ones) hold identically and exactly; the 4×4 symbolic Jacobian determinant is identically 1; and the three claimed points each map exactly to their stated image. A counterexample is an existence claim, so certifying the exhibit IS certifying the claim — the only lane in this set where that is true.
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:
All claimed identities hold exactly (bracket relations, det J = 1, three-point fiber). Mutation control 1 (R -> R + 1/7): rejected, 3 failing checks. OK Mutation control 2 (bracket sign swapped): rejected, 2 failing checks. OK Elapsed: 0.4s VERDICT: CONFIRMED
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 2 were rejected in the run that built this page, and a control that stopped firing would refuse the page instead.
| the corruption, and how it was caught | |
|---|---|
| 1 | R -> R + 1/7 — rejected, 3 failing checks |
| 2 | bracket sign swapped — rejected, 2 failing checks |
The author’s surrounding prose beyond the extracted definitions. Nothing load-bearing: the counterexample stands or falls on the exhibit, and the exhibit holds.
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-poisson/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.