VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Mason conjectured the following: let $M$ be a matroid of rank $r$, and let $W_i$ denote the number of flats of $M$ of rank $i$. Is it true that for all $1 \leq i \leq r - 1$, we have $W_i^2 \geq W_{i + 1}W_{i - 1}$? This is false; a counterexample is given by a graphic matroid whose graph is a generalized theta graph with $79$ edges.
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.
What AI did
ChatGPT-5.5 Pro, Claude Opus 4.8
The author prompted ChatGPT-5.5 Pro to search for counterexamples to Mason's conjecture. After finding none on at most $9$ elements, the author expanded his search to consider matroids on large ground sets realizable over $\mathbb{F}_5$ and at failures of log-concavity at high indices. ChatGPT-5.5 Pro found a variant of the given counterexample.
ChatGPT-5.5 Pro and Claude Opus 4.8 were used for proofreading and generating the figures.
Refuting log-concavity of the flat counts is weaker than refuting their unimodality, since log-concavity is the stronger property. A counterexample to unimodality followed three weeks later and is tracked separately as Rota's Unimodality Conjecture for Matroid Flats; this paper came first.
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.