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Claim. Kahn's flow conjecture holds, and with it Chvátal's conjecture for a finite ground set, the corrected Statement of Problem 701. Theorem 1.1 of On Kahn's flow conjecture states: for an increasing antipodal $h:2^{[n]}\to\mathbb{R}$ and nonnegative weights $\lambda_T(i)$, $i\in T$, summing over $i$ to $\hat h(T)^2$ for each nonempty $T$, the linear function $L_\lambda(x)=\sum_i\lambda_ix_i$ with $\lambda_i=\sum_{T\ni i}\lambda_T(i)$ flows upward to $h_+^2$. Taking $h=2\cdot1_B-1$ for a maximal intersecting family $B$ gives Kleitman's conjecture, that every intersecting subfamily of a downset $D$ has weight at most the weight of some star for every nonnegative nonincreasing weight, and the unit weight gives Chvátal's conjecture. The paper first recasts the proof of Chvátal's conjecture by Chang, Liu and Liu (claim page) in Halmos's theory of two subspaces, sharpening their analytic bounds and deriving equality and stability properties, and then proves Kahn's conjecture by replacing dimension counting with singular value estimates for a weighted operator. It reproves the monomial calculation of that preprint (its Proposition 3.2) and credits it with the first proof, so it is a complete argument with a stronger conclusion that rests on ideas of the earlier one, as its author states.

Depends on. No page of this wiki: the paper proves, as its Proposition 3.2, the monomial dimension count it takes from Lemma 3.1 of Chang, Liu and Liu, and proves its sharpened form of their bound (Proposition 4.1) itself.

Claimant. Peter Keevash, whose statement on AI use says that the proof was found by GPT-6 Astra following an approach the author suggested, for which the preprint of Chang, Liu and Liu supplied the missing piece, and that the author simplified and rewrote the proof. The paper has no proof-claims entry of its own on the erdosproblems.com forum; the entry of 30 September 2026 for the first proof names it as related work.

Acceptance. None: the preprint is not refereed, no outside reviewer has endorsed it, and the site labels the problem OPEN (2026-10-07). The later note of Ellis, Filmus and Friedgut describes it as proving Kahn's conjecture in complete generality, which is scholarly acknowledgment and not a review record.