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Claim. The repository ipitchford/erdos-848-all-n, archived on Zenodo on 28 July 2026 as Candidate certificate-backed all-N determination for Erdős Problem 848 (version 0.1-candidate, CC0; the deposit is the archive of the repository at its tag v0.1-candidate, the commit the links above are pinned to), presents what it calls an unrefereed candidate computer-assisted proof that for every $N\ge1$ the largest size of a set $A\subseteq\{1,\ldots,N\}$ with $ab+1$ never squarefree for $a,b\in A$, the diagonal $a=b$ included, is

$$\left\lfloor\frac{N+18}{25}\right\rfloor,$$

the number of members of the class $7\bmod25$; so the answer to Problem 848 is yes for every $N$. The lower bound is the class itself. The README at the pinned commit assembles the upper bound from five overlapping ranges: exact coloring certificates with an endpoint induction for $N\le10^8+6$; an exhaustive structural split with exact replays for $10^8\le N\le10^9$; exact-rational short-shift envelopes for $10^9\le N\le10^{12}$; exact-rational rank envelopes for $10^{12}\le N\le2.64\cdot10^{17}$; and, for $N\ge2.64\cdot10^{17}$, the explicit threshold theorem of Sothanaphan 2026, whose note the replay script requires by its checksum and does not bundle. The README calls this a value theorem that does not claim the uniqueness of the extremal sets, and states its own assurance boundary: the finite and structural ranges rest on certificate replays with mutation and sanitizer controls, the high range on the cited analytic theorem plus a numerical replay of its constants, and no independent external reproduction, external peer review or end-to-end kernel formalization exists. This page rests on the Zenodo record and the README; the paper (paper.pdf in the repository) was not read.

Provenance. The Zenodo record lists OpenAI Codex as the creator and Ian Pitchford as project leader; the record and the README describe the proof, replay and audit development as the work of an OpenAI Codex workflow, as reported by the repository's own history, and the problem selection, research direction, mediation, repository maintenance and publication as Pitchford's. The human publisher is the claimant of this page, with the system named as the record names it. The repository's progress bundle is dated 27 July 2026, and its README records the site's problem page as accessed; the Zenodo publication of that day is the first posting found. The result predates the release of Li's full claim of 30 July 2026, which reaches the same value by a different route.

Acceptance. None on record. The result was not submitted to the site's proof-claim tab; it reached the site through a forum comment of 19 August 2026 on Li's claim (linked above), whose writer reports recomputing the envelopes' constants exactly, replaying the per-interval checks with ablation controls, and finding the coverage of the ranges gapless, and concludes that two independent methods agree on the value. The site's label is DECIDABLE for Sawhney's result (page last edited 6 December 2025, before this result), and the curator has not acted on it; no referee or named expert has examined it, and nothing was downloaded, replayed or audited here. A forum comment is neither a named reviewer nor a referee, so no evidence is listed. The claim stays claimed, and the problem's standing is claimed, proved, through this page and Li's agreeing full claim.

Depends on. Sothanaphan 2026 for every $N\ge2.64\cdot10^{17}$, a pending partial claim; this claim stands or falls with it on that range.