Newer public claim (6 Oct 2026): OpenAI's internal-model release claims, for this problem, r_k(N) ≤ C_k·N·exp(−c_k(log N)^ε_k) for every k ≥ 3 (quasipolynomial Szemerédi), hence the reciprocal-sum conjecture — family 159 at
github.com/openai/math, OpenAI's own Lean proves the reciprocal-sum statement — Erdős #3 exactly as asked — via a weaker bound r_k(N) ≤ C·N·exp(−c(log log N)^(1+η)) (itself new past the summability threshold); the quasipolynomial headline is paper-only; kernel-replayed on our machine (standard axioms, statement matched) — see our /day entry. Bloom calls these claims, not endorsements; anything on this page that says the question is open was written before that release and has not re-checked it.
SKIP: Live page status is OPEN - $5000 (accessed 2026-07-26), but it lists dbmcdonough under “Currently working on this problem” (0 claimed proofs; “Interested in collaborating”: None), so the mandatory no-collision rule applies.
This is the AI working report, labelled by outcome — not an
independently verified claim unless marked PROVED. ← our attempt log · problem #3