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Claim. The answer to Problem 7 is no, under one unproved hypothesis. The Lean file main.lean of the repository posted on the problem's discussion thread on 2026-01-11 by the users gebyjaff and AlejandroZarzuelo, pinned above at its commit of that day, proves erdos_selfridge_answer: there is no covering system with distinct odd moduli, given the hypothesis HoughNielsenFact that every distinct covering system has a modulus divisible by $2$ or $3$. That hypothesis is the published theorem of Hough and Nielsen, accepted on its claim page. The file also declares the axiom HoughNielsenGoodFibre: for an odd covering system with a modulus divisible by $3$ and not every exponent trivial, the union of two finite obstruction sets in $\mathbb Z/3^e\mathbb Z$ is smaller than the whole group. The post says the proof was generated with Archivara and Aristotle, with a human bridging the final gap, and the file's header says it was edited by Aristotle; a PDF appendix gives sources for the second axiom.

Hypothesis. The axiom HoughNielsenGoodFibre, a quantitative fibre bound the appendix attributes to the Hough–Nielsen method. It is not a published theorem, and nothing on the thread or in the repository proves it. If it holds, the development derives the negative answer; the claim decides nothing without it.

Depends on. The Hough–Nielsen theorem on its claim page, which the development takes as its hypothesis HoughNielsenFact.

Standing. Claimed. The thread's replies of 2026-01-11 found gaps: Daniel Larsen asked for the missing explanation of how Hough and Nielsen's uncovered set relates to the collision events the file uses and why the active moduli stay distinct; Nat Sothanaphan judged the appendix to be machine-generated; and a user reported that the development leaves holes Aristotle did not fill. The claimants did not withdraw. There is no write-up beyond the appendix, no refereed publication, no outside review, and this corpus has not built the development; the site's label for the problem is VERIFIABLE.