Significance recordshttps://hjyuh.github.io/significance/feed.xml2026-10-01T13:17:58ZWe prove that this graph contains an infinite simple path, answering Erdős Problem 1212 affirmatively. More precisely, for almost every slope in a fixed interval away from the diagonal, there is a ray with that limiting coordinate ratio.https://hjyuh.github.io/significance/2026-alexchengyuli-erdos-1212/2026-09-09T00:00:00ZRecord v1; 6 evidence entries; 1 open invitations.The 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 v3; 1 evidence entries; 3 open invitations.A Tilted Residue-Class Construction for Long Prime-Free Intervals claims Y(X) ≫ X log X / log₃ X and G(T) ≫ log T log₂ T / log₄ T.https://hjyuh.github.io/significance/2026-dottedcalculator-erdos-4/2026-08-31T01:02:46ZRecord v1; 3 evidence entries; 3 open invitations.The paper claims that for every sufficiently large integer k there is an integer n with k + 1 < n < L_k = lcm(1,...,k) such that no prime p <= k divides binom(n,k). Consequently g(k) < L_k eventually.https://hjyuh.github.io/significance/2026-ethanyang-erdos-1095/2026-10-01T13:17:58ZRecord v1; 3 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.For every 3-graph G on n ≤ 9 vertices, |E(G)| − 3ν(G) ≤ ex₃(n, K₄³). Equivalently, every such G admits an edge-disjoint decomposition into at most ex₃(n, K₄³) single triples and tetrahedra.https://hjyuh.github.io/significance/2026-rafikzeraoulia-erdos-719/2026-09-09T00:00:00ZRecord v1; 6 evidence entries; 1 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.