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Claim. The note proves the Erdős--Sós conjecture, that a graph with average degree greater than $t-2$ contains every tree on $t\ge2$ vertices, which with $t=k+1$ is a strict-threshold form of the statement of Problem 548 and implies it. Its abstract says that the conjecture was recently proved by GPT-6 Astra and that the note presents a simplified version of that argument in a more natural form; the note also determines the extremal graphs, and proves the related conjecture of Addario-Berry, Havet, Linhares Sales, Reed and Thomassé on antidirected trees in digraphs, again with its extremal graphs.

Claimant and postings. Oliver Riordan and Alex Scott, A short proof of the Erdős--Sós Conjecture, arXiv:2609.15893, v1 14 September 2026 (the date this page is named by) and v2 16 September 2026. A comment of 19 September 2026 in the site's discussion lists it. The argument is the authors' simplification of the proof recorded on Adamczewski 2026, whose Reviewed account cites this note.

Standing. Claimed, not accepted: a preprint, not refereed, reviewed or formalized.

Depends on. Nothing in this wiki.

Read depth. The arXiv abstract and version record were read; the body was not.