Problem detail · source-aware
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The Foregger–Sinkhorn tie-point conjecture, Conjecture 41 in Minc's survey, asserts that if a nearly decomposable doubly stochastic matrix minimizes the permanent on a face and the permanental cofactor at a prescribed zero exceeds its permanent, then that zero is a tie point. False: an explicit $8 \times 8$ counterexample exists, built on the unique root $\beta$ of $7t^3 - 13t^2 + 12t - 4$ in $(59/100, 3/5)$.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
The paper's acknowledgement, in full: "The proof of Theorem 1 was carried out by GPT-5.6-sol and Claude Fable 5, under the guidance of the author. The author has reviewed the resulting proof arguments. Responsibility for the final text rests with the author."
Provider: OpenAI, Anthropic · Prompt public: unknown · Independence: unknown
Independently recomputed by this site on 21 August 2026 from the paper's own data (arXiv:2608.13025v1), at 60-digit precision: $\beta$ is the unique root of the stated cubic in the stated bracket, on which the cubic is monotone; the matrix is doubly stochastic and nonnegative; its 19-entry support is nearly decomposable, being fully indecomposable while the removal of any single support entry destroys that; the permanent agrees with the paper's closed form to 1e-61; the cofactor gap agrees with its closed form to 4e-61 and exceeds the claimed 2047/240100; and the prescribed zero is not a tie point, with exactly one witnessing support entry. The conjecture's hypothesis also holds: the face is four-dimensional, and a 6561-point grid plus 61 local descents found nothing on it with a smaller permanent. Still a days-old preprint with no independent review, hence a candidate.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.