What was already known
Daykin and Frankl posed the relative-width inequality in 1983. The manuscript says it was previously known for binary downsets, citing Duffus, Howard and Leader (2019), but not for arbitrary convex subsets. Williams's stronger product inequality is the inductive statement used to prove the conjecture (introduction and Theorem 1).
AI involvement
Williams explicitly credits ChatGPT 5.6 Sol Pro with generating the proof content. Williams selected and understood the problem, checked the argument, and wrote the note; no independent model run is documented.
Williams says ChatGPT 5.6 Sol Pro generated the proof content. Williams selected and checked the problem and communicated the argument; no independent model run is documented.
- Supporting source (arxiv.org) — Abstract and §4 Acknowledgements
Importance
The reported argument resolves a longstanding extremal-poset conjecture and supplies a stronger product inequality for convex Boolean-lattice subsets.
Limitations
This is a four-page unrefereed preprint. Williams says he verified and communicated the model-generated proof, but does not describe a separate completed proof audit or formal check. The claim is assessed as reported, pending an independent mathematical reading.
Technical verification
The abstract says Williams verified the model proof of the conjecture, and the note gives a complete written argument, but it does not document the checking method for the stronger product inequality selected here or an independent completed review.
Human understanding
Williams explains the backward induction, the convexity lemma and its antichain construction, providing a human-readable account of the central mechanism for the selected product inequality.
Correction and publication history
Claim-level review of the primary manuscript for non-notifying local inclusion.
Read this published revision