algebra / Affine Algebraic Geometry, Polynomial Maps

A Five-Variable Counterexample to the Hessian Conjecture

Registry resolution: resolved. Reported result type: disproved. The registry record and named primary source provide the statement and scope.

30Significance / 100
2Frontier events
0Verification tasks
1Recorded attempts

Temporal state

Current frontier

Replayed

Explicit construction artifact replay passed; symbolic determinant proof remains source-level

Append-only history

Frontier timeline

algebraAug 29, 2026Significance 74/100

Five-variable Hessian counterexample artifact replay passed

Prior state unknown→Explicit construction artifact replay passed; symbolic determinant proof remains source-level

The pinned no-CAS checker reproduced the degree, monomial count, exact rational gradient collision, and deterministic exact Hessian evaluations. VibeMathed's external label remains unreviewed; this is a separate local replay record.

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Replayed

The published polynomial Ψ=A²+13A+2B expands to 42 monomials of degree 14, has the reported rational gradient collision, and returned Hessian determinant 128 at all 40 deterministic exact test points in the no-CAS checker.

This is an artifact replay of the authors' checker at pinned commit 7b23ada. The finite exact evaluations do not replace the paper's symbolic determinant proof.

Source authenticated

Registry resolution: resolved. Reported result type: disproved. The registry record and named primary source provide the statement and scope.

Recorded attempts

Run the pinned no-CAS Hessian checker

success · MFN independent verifier

All checks passed, including the exact rational collision and deterministic Bareiss determinant evaluations.

Evidence graph

Connected research record

A Five-Variable Counterexample to the Hessian Conjecture — Mathematical Frontier Network