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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

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Claim. h3(4)=71h_3(4)=71 in the notation of Problem 934: every graph of maximum degree at most 44 with at least 7171 edges has two edges at distance at least 33, and the odd graph O4O_4, with 7070 edges, has none. The claim was posted on the problem's discussion thread on 17 August 2026 (18:25) under the account BitterLemma and published the same day as a Zenodo manuscript, Maximum line subgraphs of diameter three at maximum degree four: h3(4)=71h_3(4)=71, by the Bitter Lemma project (CC BY 4.0), with a Lean 4 development in the repository bitterlemma/erdos-934. The lower bound is Kumar, Mohar and Pragada's (their claim page), whose Lemma 3.1 the repository says it formalizes from the preprint's own argument. The upper bound, as the post and the README describe it, is an elementary finite reduction confining any extremal configuration to at most 8080 vertices in four breadth-first layers from a base edge, a counting bound leaving at most 7979 edges, and an exhaustive certified search over 123123 surviving layer profiles. The README says that the reduction, the counting bound, the exhaustiveness of the case split, the symmetry breaking, the completeness of the propositional encoding, the witness and the assembly are proved in Lean 4 (toolchain v4.33.0 with Mathlib) without sorry on the axioms propext, Classical.choice and Quot.sound, and that the only input from outside the proof assistant is the unsatisfiability of 123123 explicit CNF formulas, each with an LRAT refutation; the headline theorem H34.Complete.h_three_four_of_encode carries that unsatisfiability as an explicit hypothesis. The post's and the record's provenance statement says that the mathematics, code, formalization and text were produced with Claude (Anthropic) under human direction and review, and that every externally checkable component was verified by a pass independent of the one that produced it.

Covers. The single value h3(4)=71h_3(4)=71, the first exact value of h3(d)h_3(d) beyond h3(3)=23h_3(3)=23. Not covered: any other (t,d)(t,d) with t≥3t\ge3, the asymptotics of h3(d)h_3(d), and the problem's request for an estimate of ht(d)h_t(d) in general.

Depends on. Kumar, Mohar and Pragada for the lower bound h3(4)≥71h_3(4)\ge71, which the manuscript takes from the preprint; the upper bound is the manuscript's own.

Standing. Claimed. The manuscript is a Zenodo deposit with no refereed version, the site's label is OPEN (2026-10-06) and its proof-claim tab does not list the result, and no referee, named reviewer or outside build of the Lean development is recorded. The development is not Lean this corpus built or audited, so the page lists no formalized evidence; the repository's statements about its axioms and certificates are recorded as its own.