Claims

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2026_01_17_chojecki: Chojecki's claimed proof of 17 January 2026, a dyadic deletion scheme with the algorithmic local lemma, rewritten on 19 January after commenters found errors the author acknowledged; replaced by their different proof of July 2026.

2026_06_28_sharma: Sharma's greedy-scan proof, first posted to GitHub on 28 June 2026 and claimed on the site on 26 July, with a Lean file resting on three literature results taken as axioms; made with Claude, reviewed by nobody, not built here.

2026_07_10_kielhorn: Kielhorn's Zenodo preprint of 10 July 2026 claims a density-one set with distinct consecutive products by a sparse deletion scheme on prime gaps; linked from the thread by the curator, not read in detail, reviewed by nobody.

2026_07_13_chojecki: Chojecki's gap-greedy construction over consecutive primes gives a set of density one with all consecutive-block products distinct, answering yes; an AI-assisted proof of 13 July 2026, accepted by the site after Pratt's digest.

2026_07_13_pauwels: Pauwels's proof attempt, dated 10 July 2026 and linked from the thread by the site's curator on 13 July, claims the density-one set by a construction Chojecki found similar to their own; made with GPT-5.6 Sol, reviewed by nobody.

2026_07_21_sneiderman: Sneiderman's note of 21 July 2026 reproves Chojecki's density-one construction with short rejected gaps bounded by X^{43/50+o(1)}; posted as a site proof claim, made with GPT 5.6 Sol Ultra, followed by Pratt's digest.

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