Sharp logarithmic exponents for off-diagonal Ramsey numbers

What OpenAI claims

For every fixed integer s ≥ 5, proves r(s,t)=t^s-1/(log t)^s-2+o(1) as t → ∞, determining the logarithmic exponent and matching the classical upper bound at that scale. Here r(s,t) is the least number of vertices forcing an s-clique or a t-vertex independent set. (Lean)

Papers (2)

1. The sharp logarithmic exponent of r(5,t)

   24 September 2026 · Preprint, not peer reviewed · PDF

   We determine the sharp logarithmic exponent of the off-diagonal Ramsey number r(5,t):

2. Sharp logarithmic exponents for fixed off-diagonal Ramsey numbers

   24 September 2026 · Preprint, not peer reviewed · PDF

   For every fixed integer s ≥ 6, we determine the sharp logarithmic exponent of the off-diagonal Ramsey number:

Status

Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.