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Claim. The optimal constant $c$ of Problem 36, the minimum overlap constant, satisfies $c\le0.380876$. The result is reported in Section 4.1.1 of M. Yuksekgonul, D. Koceja, X. Li, F. Bianchi, J. McCaleb, X. Wang, J. Kautz, Y. Choi, J. Zou, C. Guestrin and Y. Sun, Learning to Discover at Test Time, arXiv:2601.16175 (22 January 2026), cited as [YKLBMWKCZGS26] on the problem page from the copy on the authors' project site, both linked above; the arXiv version is digested on the library card yuksekgonul_2026_learning_discover_test_time. By Swinnerton-Dyer's reformulation, as Haugland reports it, a step function $f$ on the scaled interval with values in $[0,1]$ and integral $1$ gives an upper bound on $c$ without an explicit partition, subject to the constraints $f(x)\in[0,1]$ and $\int f=1$. The paper's search method, which it calls TTT-Discover and which trains a language model by reinforcement learning at test time, produced a 600-piece asymmetric step function whose functional value is $0.380876$, below the symmetric 95-piece function of AlphaEvolve with value $0.380924$ [GGTW25] and Haugland's 51-piece function with value $0.380927$ [Ha16]; the site's commentary credits the record upper bound to the TTT-Discover LLM, and the claimants are the paper's authors. The construction is said to be released with the authors' code; the PDF does not print the step function, and no certificate is held in this corpus. Section 4.1.4 of the paper carries an invited reviewer's paragraph saying that such a bound is straightforward to verify by evaluating the functional at the finitely many points determined by the breakpoints and checking the norm constraints; that is a statement in the paper, not a check made here.

Covers. The upper bound alone: $c\le0.380876$. The claim does not determine $c$ and says nothing about the lower bound; a later certified upper bound, $0.38085906$, is on Russell's claim page.

Depends on. No page of this wiki.

Standing. Claimed. The paper is a machine-learning preprint with no refereed publication recorded; the site's curator credits the record upper bound to it in the problem page's commentary (label OPEN, page last edited 23 January 2026), which is not acceptance of a result; the certificate is outside the PDF and is not recomputed here.