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Claim. The optimal constant $c$ of Problem 36, the minimum overlap constant, satisfies

$$c<0.3808590568145606537807120$$

(Theorem 7), and the simpler certificate of Theorem 6 gives $c<0.3808594223653146192081122$. The result is K. Russell, A tighter upper bound for the Erdős minimum overlap constant, Zenodo record 21327851 (release v1.2, dated 2026-07-12), digested on the library card russell_2026_tighter_upper_bound_erdos_minimum_overlap_constant. Lemma 1 of the paper shows that for an $N$-cell step function the overlap is piecewise linear in the shift and that its supremum equals $(2/N)\max_m\sum_if_ig_{i+m}$, where $g_j=1-f_j$ for $1\le j\le N$ and $g_j=0$ otherwise, so finitely many exact rational correlations certify an upper bound. Theorem 6 evaluates an admissible $N=1024$ vector due to Hyra after exact rational normalization, with the maximum at lag $-266$; Theorem 7 evaluates an $N=512$ vector that the paper attributes to lnzwz_AI4M_Agent, as it names the system, after adding the vector's exact mass deficit $192252155\cdot2^{-78}$ to one cell, since the raw vector fails exact normalization and uniform rescaling would exceed the allowed value $1$ in saturated cells. The identity between the discrete constant and the function-space infimum is quoted from earlier work, not proved. The paper's Section 5 examines White's convex program numerically and, as it says, establishes no new lower bound.

Covers. The upper bound alone: $c<0.38085906$, below the site's record $0.380876$ on the TTT-Discover claim page. The claim does not determine $c$ and says nothing about the lower bound.

Depends on. No page of this wiki.

Standing. Claimed. The paper is a self-published Zenodo release with no refereed version or outside review recorded; the site's commentary, last edited 23 January 2026, predates it and gives $0.380876$ as the record upper bound.