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Claim. The optimal constant $c$ of Problem 36, the minimum overlap constant, satisfies $c\ge0.379005$. This is Theorem 1 of E. P. White, A new bound for Erdős' minimum overlap problem, Acta Arith. 208 (2023), no. 3, 235–255, posted on arXiv on 2022-01-14 as arXiv:2201.05704 under the title Erdős' minimum overlap problem and cited as [Wh22] on the problem page; the arXiv version is digested on the library card white_2022_erdos_minimum_overlap_problem. White works with the continuous form of the problem due to Moser and Murdeshwar, whose value Swinnerton-Dyer showed equals $c$: minimize $\sup_xM(x)$ for $M(x)=\int f(t)g(x+t)\,dt$ over measurable $f:[-1,1]\to[0,1]$ with $g=1-f$ and $\int f=1$. Elementary Fourier analysis gives linear and quadratic constraints on the Fourier coefficients and the moments of $M$ (Lemmas 2–7), the constraints define a convex program (Section 5, (5.1)–(5.13)) whose feasible set contains every admissible $M$ (Proposition 9), and a numerically computed dual bound for that program is the theorem. It replaced Moser's $\sqrt{4-\sqrt{15}}=0.3563\ldots$ as the best lower bound, and the site's commentary records it as the lower side of the current records.

Two cautions, recorded on the library card from the printed text of the arXiv version: constraints (5.6)–(5.7) carry the factor $8/(m\pi)$ where (3.6) gives $B_m=-\frac4{m\pi}\sin(m\pi/2)\,b_m$, and the tail bounds (5.8)–(5.9) write $m$ where Proposition 9 defines the tail variables at the odd index $2m-1$, so the feasibility argument of Proposition 9 does not follow literally as printed; Russell's paper on Russell's claim page (Remark 9) notes the same index slip in (5.8)–(5.9). The paper also prints no fully checkable certificate: the dual assignments are offered on request (Section 5.1). Neither point is a published erratum; the journal text is not held, so whether the published version corrects the formulas is unknown.

Covers. The lower bound alone: $c\ge0.379005$, a non-strict inequality. The claim does not determine $c$ and says nothing about the upper bound. Later claimed lower bounds are on the pages of Kim and Pilanci, Price and Drynshock.

Depends on. No page of this wiki.

Acceptance. Refereed: Acta Arithmetica 208 (2023), no. 3, 235–255, doi:10.4064/aa220728-7-6, the DOI linked above; the arXiv posting of 2022-01-14 names the page. The site's curator, Thomas F. Bloom, credits the record lower bound to White [Wh22] in the problem page's commentary (label OPEN, page last edited 23 January 2026); the problem is not marked settled, so the credit is not listed as reviewed. The printed-formula inconsistencies above are observations on the arXiv text recorded on the library card, not a review, and the proof is not checked in this corpus.