Problem detail · source-aware
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
For the set of $n \times n$ doubly stochastic matrices, Kim and Roush conjectured in 1981 that for odd $n = 2k+1 > 1$ the maximum of $\mathrm{per}(I-A)$ equals $3 \cdot 2^{k-2}$, attained by an explicit block construction. Proved in full, and the maximizers are classified: they are exactly the simultaneous-permutation conjugates of that construction.
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 acknowledgments are one sentence and leave nothing to interpret: "The proof of this conjecture 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
A preprint days old, with no independent review.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Kim and Roush did not claim uniqueness; the classification of equality cases is new alongside the conjecture itself.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.