---

Claim. Junichiro Fukuyama, The Sunflower Conjecture Proven, arXiv:2212.13609v3, claims an absolute constant $C>0$ such that every family of sets of size at most $m$ with more than $(Ck^4)^m$ members contains $k$ distinct sets with a common pairwise intersection. For positive $n$ and fixed $k$, specializing to $n$-uniform families and enlarging the base gives the strict exponential bound asked in Problem 20.

Covers. The full displayed sunflower conjecture.

Source and standing. The arXiv record was read on 2026-10-15 UTC at abstract and version-history depth. It dates the first version to 27 December 2022 and version 3 to 22 June 2026; the version-3 comment says it fixes an error in version 2. The date in this page's name is the first public posting, while the linked statement is version 3. No independent proof examination or acceptance evidence is established by this record. The claim is pending and is not an established premise for the research recorded here.

Depends on. The cited version-3 preprint. Its proof has not been checked here, and no project theorem or formal verification is asserted.