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Parikshit Chalise, Antwan Clark and Edinah K. Gnang, A Proof of the Tree Packing Conjecture, arXiv:2410.13840 (v1 17 October 2024, v2 23 October 2024, v3 1 September 2026; record as of 2026-09-19); the paper's text is not held, and the claim is recorded from its abstract and the thread's account of it.

The claim. The answer to Problem 743 is yes for every $n$: whenever $T_k$ is a tree on $k$ vertices for $k=2,\ldots,n$, the complete graph $K_n$ is the edge-disjoint union of copies of $T_2,\ldots,T_n$. The abstract claims this by a polynomial method and a reformulation of a packing as a "complete labeling"; the site's thread (a comment of 28 February 2026) outlines the paper's route through augmented functional trees, a polynomial certificate, its Proposition 3.4, its Composition Lemma 3.10 and its Theorem 1.9.

Depends on. Nothing in this wiki.

Standing. Withdrawn by its authors: version 3 of the arXiv record carries the comment "Withdrawn due to an error in the proof of Lemma 3.10 (Composition Lemma), which was based on the argument in arXiv:2202.03178v2". The claim was never accepted. The thread's comment of 28 February 2026 found no refereed version and no independent verification, a comment of 1 March 2026 reported that people who had tried to verify the paper did not trust its arguments, and another of the same day reported a GPT-based check, as its poster names it, that flagged two major gaps; the search of 2026-09-19 found no acceptance either, and the site's page, as of 2026-09-19, did not mention the claim. The problem's standing is unaffected.