Claims

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1977_01_01_spencer: Spencer's Theorem 2.1, R(3,t) at least (1/27 - o(1))(t/ln t)^2, from the local lemma, which proves the case s = 3 with c(3) = 2; refereed in Discrete Mathematics (1977).

2023_06_06_mattheus_verstraete: Mattheus and Verstraete's Theorem 1, r(4,t) at least a constant times t^3 over the fourth power of log t, which proves the case s = 4 with c(4) = 4; refereed in the Annals (2024).

2026_06_16_bradac: Bradač's Theorem 1.1 gives, for every fixed s at least 3, the lower bound r(s,k) at least c_s k^{s-1}/(log k)^{2s-4}, which answers the problem with c(s) = 2s-4; an arXiv preprint accepted by the site's curator, not refereed.

2026_09_24_openai: Two manuscripts of the OpenAI mathematics release prove r(s,t) = t^{s-1}/(log t)^{s-2+o(1)} for s = 5 and for every fixed s at least 6, accepted as a partial answer on the two Lean declarations the corpus's verification built and audited; the manuscripts are unreviewed.

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