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Claim. The optimal constant $c$ of Problem 36, the minimum overlap constant, satisfies $c\ge0.37912$ (Section 4.2, Table 1). The result is reported by S. Kim and M. Pilanci, AI-Assisted Discovery of Convex Relaxations via Dual Agents, arXiv:2606.31182 (30 June 2026), digested on the library card kim_pilanci_2026_ai_assisted_discovery_convex_relaxations_via_dual_agents. The paper's Algorithm 1 augments White's convex program with the positive-semidefiniteness of the Toeplitz matrix $T_f$ of the admissible function and of $I-T_f$ (Proposition A.1, (15)–(16)), necessary conditions that follow from $0\le f\le1$; a subdivision of parameter boxes supplies local bounds whose minimum covers the admissible range (Section 4.1, Appendix E), and conic duality with directed rounding (Theorem C.1) certifies each local bound against the dual residual and the data error. The paper describes its method as a coding agent that proposes constraints, a theory agent that checks them and looks for counterexamples, and a human who reviews the final programs (Sections 3.3 and 4.3); the validity of the constraints rests on the paper's arguments and that review, not on formal verification. The identification of the function-space constant with $\lim_nm(n)/n$ is cited background, not proved in the paper. The library card notes that the normalization of the Toeplitz matrix in (15) and the quadratic form printed in Proposition A.1 are not reconciled in the arXiv text.

Covers. The lower bound alone: $c\ge0.37912$, strictly above White's $0.379005$. The claim does not determine $c$ and says nothing about the upper bound; the later and larger claimed lower bounds of Price and Drynshock have their own pages.

Depends on. White's claim page: the program this result strengthens is White's relaxation (White's Section 5 constraints), so the validity of those constraints, including the printed-formula cautions recorded there, is an input to this bound.

Standing. Claimed. The paper is a preprint with no refereed publication or outside review recorded; the site's commentary, last edited 23 January 2026, predates it and gives White's $0.379005$ as the record lower bound.