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Claim. The optimal constant $c$ of Problem 36, the minimum overlap constant, satisfies $c>0.3805634$. The claim was submitted to the site's proof-claims tab on 2026-09-19 by the forum user Drynshock as a partial proof credited to GPT 6 Pro, with a write-up in a shared folder linked above. Its summary describes the new ingredient: for an admissible overlap profile $h$, with $p(t)=\int h(x)(1-h(x+t))\,dx$ and $F(t)=p(t)+p(-t)$, the inequality

$$F(s+t)\le F(s)+F(t)\qquad(s,t\ge0,\ s+t\le2)$$

holds; integrating this subadditivity gives linear constraints on the admissible profiles, which are added to the Fourier and moment relaxation behind the earlier lower bounds, and the strengthened relaxation yields a certified bound. 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), slightly above the claimed $0.38055470$ on Price's 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). The inequality and its use are taken from the claim's summary.

Submission note. Posted to erdosproblems.com as a proof claim by Drynshock (account drynshock) on 19 September 2026, giving "GPT 6 Pro" as the AI used:

We prove the improved lower bound

$$\boxed{\mu>0.3805634}.$$

The main new

ingredient is the following structural inequality. If

$$p(t)=\int > h(x)(1-h(x+t))\,dx$$

and

$$F(t)=p(t)+p(-t),$$

then for all $s,t\ge0$ with

$s+t\le2$,

$$\boxed{F(s+t)\le F(s)+F(t).}$$

Integrating this subadditivity

relation gives new linear constraints on admissible overlap functions, which strengthen the previous Fourier/moment relaxation and lead to the certified bound above.

Covers. The lower bound alone: $c>0.3805634$. The claim does not determine $c$ and says nothing about the upper bound.

Depends on. White's claim page: by the claim's summary, the new constraints are added to the earlier Fourier and moment relaxation, which is White's program, so the validity of White's constraints, with the cautions recorded there, is an input to this bound.

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.