Significance recordshttps://hjyuh.github.io/significance/feed.xml2026-08-24T08:54:00ZThe submission claims a full proof that, for every N >= 1, the maximum size of a set A subset of {1, ..., N} such that ab + 1 is nonsquarefree for every a, b in A is floor((N + 18)/25).https://hjyuh.github.io/significance/2026-alexchengyuli-erdos-848/2026-08-22T15:00:00ZRecord v1; 3 evidence entries; 3 open invitations.lim inf as T → ∞ of N₀*(T, 2T) / N(T, 2T) ≥ 3/2 − (1/√2) cot(1/√2) = 0.67250… .https://hjyuh.github.io/significance/2026-anthropic-zeta-two-thirds/2026-08-11T12:00:00ZRecord v2; 1 evidence entries; 3 open invitations.The submission claims a proof of the first assertion of Erdős Problem #132 for n = 8: every eight-point planar set has two distinct distances occurring at most eight times.https://hjyuh.github.io/significance/2026-evanbeller-erdos-132/2026-08-24T08:54:00ZRecord v1; 2 evidence entries; 2 open invitations.The unit group L_F2(1,2)× of the binary Leavitt algebra is not sofic.https://hjyuh.github.io/significance/2026-openai-nonsofic-groups/2026-08-11T12:00:00ZRecord v8; 2 evidence entries; 3 open invitations.The manuscript gives a partial result toward Erdős Problem #653, proving an improved upper bound g(n) ≤ n − 1 − cε n^(0.81668−ε).https://hjyuh.github.io/significance/2026-rafikzeraoulia-erdos-653/2026-08-18T05:08:00ZRecord v2; 1 evidence entries; 3 open invitations.The paper proves Problem #726 conditionally on an explicitly stated reciprocal-prime equidistribution hypothesis.https://hjyuh.github.io/significance/2026-rafikzeraoulia-erdos-726/2026-08-18T05:08:00ZRecord v2; 2 evidence entries; 4 open invitations.