Problem detail · source-aware
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White conjectured that the symmetric exchange binomials generate the toric ideal of a matroid. This is now known to be false; a rank $9$ binary matroid constitutes a counterexample.
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 author prompted ChatGPT-5.5 Pro to check White's conjecture and it claimed to prove the result for ranks $5$ and $6$. After further prompting to check for random matroids of ranks $7$, $8$, $9$, and $10$, it found a matroid isomorphic to the given counterexample. ChatGPT-5.5 Pro and Claude Opus 4.8 were used for proofreading and generating the figures.
Provider: OpenAI; Anthropic · Prompt public: unknown · Independence: unknown
arXiv preprint with explicit binary matroid construction; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. 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.