Proved here; the site's label is OPEN (page last edited 23 January 2026). The OpenAI release's manuscript The joint Dickman law for consecutive integers (2026-09-24) claims that the normalized largest prime factors of $n$ and $n+1$ have independent Dickman limit laws in natural density and deduces from that the density $1/2$ this problem asks for. Its Lean proof of that corollary was built by this corpus with only the three standard axioms, its fingerprint identical to the release's comparator challenge, and the statement audit found it exact, so the claim is accepted on the release's joint Dickman law and the problem stands solved; the manuscript has no outside review. Wang [Wa21] proved the density under the Elliott–Halberstam conjecture for friable integers, an accepted conditional claim, Wang 2021, which settles no standing.