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Claim. The optimal constant $c$ of Problem 36, the minimum overlap constant, satisfies $c\ge0.38055470$. The claim was submitted to the site's proof-claims tab on 2026-07-20 by Liam Price as a partial proof credited to GPT Pro; its summary says only that the system improves the lower bound to that value. The posting links a write-up hosted on Overleaf and, in its notes, a repository described as a reproducible certificate packet, both linked above, the repository at its commit of 2026-07-01, the last before the posting. The value lies above the refereed lower bound $0.379005$ of White (claim page) and the reported $0.37912$ of Kim and Pilanci (claim page), and below the upper bounds $0.380876$ of TTT-Discover, the site's record (claim page), and $0.38085906$ certified by Russell (claim page); if correct it would narrow the gap between the two sides to about $0.0003$. The write-up and the certificate packet are linked above; this page does not describe the method.

Submission note. Posted to erdosproblems.com as a proof claim by Liam Price (account Leeham) on 20 July 2026, giving "GPT Pro" as the AI used:

GPT Pro improves the lower bound to 0.38055470. Notes: The reproducible certificate packet can be found here.

Covers. The lower bound alone: $c\ge0.38055470$. The claim does not determine $c$ and says nothing about the upper bound.

Depends on. No page of this wiki.

Standing. Claimed. The site's label is OPEN and its commentary, last edited 23 January 2026, gives White's $0.379005$ as the record lower bound and does not mention this claim; the claim had no comments on its thread as of 2026-10-06. No outside review, refereed publication or formalization is known. A later and slightly larger claimed bound by another submitter has its own claim page.