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Claim. E. Dyachenko's preprint Constructive Proofs of the Erdos-Straus Conjecture for Prime Numbers with P congruent to 1 modulo 4 (arXiv:2511.07465v1, 7 November 2025) states as its central result that for every prime $P\equiv1\pmod4$ there are positive integers $A,b,c$ with

$$\frac4P=\frac1A+\frac1{bP}+\frac1{cP},$$

constructed by the second of two methods the abstract describes: a factorization identity with a nonlinear parametrization, and a linear system whose solutions form an affine lattice; the abstract also announces algorithms transforming one solution into another and a computational verification. The page records the claim as full because it closes the only open case of Problem 242: for a prime $p\equiv3\pmod4$ the identity $\frac4p=\frac1{(p+1)/4}+\frac1{p(p+1)/4}$ gives a representation, a solution for a prime scales to every multiple of it, and the problem page's Formulation records how a representation with repeated or fewer than three terms becomes one with three distinct terms. So a proof for the primes $P\equiv1\pmod4$ would prove the conjecture for every $n>2$.

Standing. Claimed. The arXiv listing shows a single version, not withdrawn, under a CC BY-NC-ND 4.0 license, with no journal reference and no comments field; no citing paper, review or acceptance record was found, the preprint is not on the site's proof-claim tab, and the problem's thread does not mention it. Read depth: the abstract and the arXiv record; the argument is unexamined. The site's label is FALSIFIABLE (page last edited 7 May 2026) and its commentary does not mention the preprint. The author's second 2025 preprint, arXiv:2511.17716, concerns $5/P$ and is not a claim about this problem.