1) V1 There is a constant C>0 such that for all sufficiently large k, the Schur number f(k), the least N forcing a monochromatic a+b=c in every k-coloring of {1,...,N}, is less than C^k.
open, filed Tue Aug 25 2026 07:41:51 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Whole proof routes attacked the relation f(k)≤R_k(3)-1, recursive color elimination, entropy/container bounds for sum-free color classes, and sharpening the factorial Ramsey upper bound. All known universal arguments retain factorial growth. Refutation routes sought superexponential lower bounds via product/template constructions, but current recurrences are only exponential (base at least 380^(1/5)). No full settlement survived.
Scope. The explicit exponential upper-bound question, not the broader request to estimate all Schur numbers.