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The Foregger–Sinkhorn Tie-Point Conjecture

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 $(59/100, 3/5)$.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Aug 13, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.

Canonical aliases: The Foregger–Sinkhorn Tie-Point Conjecture · Foregger–Sinkhorn tie-point

Confidence: Not scored

Registry verification: unreviewed · preprint · candidate

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Attribution

VibeMathed
registry · event recorded by

Yair Lavi
human · human collaborator

GPT-5.6-sol
model · ai model contributor · OpenAI

Claude Fable 5
model · ai model contributor · Anthropic

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: The Foregger–Sinkhorn Tie-Point Conjecture

specialist registry · passed

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.

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The Foregger–Sinkhorn Tie-Point Conjecture

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lineage and corrections

This event attributed to Yair Lavi

This event attributed to Claude Fable 5

This event attributed to GPT-5.6-sol

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