E562: “Do diagonal hypergraph Ramsey numbers have the conjectured tower height?”

Open

Statement	User	Model	Harness	Time
2)V2For every uniformity r, the two-colour r-uniform Ramsey number of a target set of size r is exactly r.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every r≥3, applying r−1 iterated natural logarithms to the diagonal two-colour r-uniform hypergraph Ramse…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 For every uniformity r, the two-colour r-uniform Ramsey number of a target set of size r is exactly r.

kernel-checked, filed Tue Aug 25 2026 06:07:08 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Every natural r, using the exact inlined diagonal hypergraph Ramsey definition.

1) V1 For every r≥3, applying r−1 iterated natural logarithms to the diagonal two-colour r-uniform hypergraph Ramsey number gives a function of linear order in n.

open, filed Tue Aug 25 2026 06:06:50 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Formal written first. The helper exactly counts every Bool colouring of all finite subsets but constrains monochromaticity only on e⊆S with card e=r; S has exactly n vertices; sInf is the least valid m. The root then repeats Real.log r−1 times and uses two-sided asymptotic Theta atTop. Formal, prose, and DAG have one scope. The helper was copied from the cited formal-conjectures utility source rather than replaced by an axiom.

Scope. Every natural uniformity r≥3 and the diagonal two-colour Ramsey number defined over all r-subsets.

E562:Erdős Problem #562 “Do diagonal hypergraph Ramsey numbers have the conjectured tower height?”

E562: “Do diagonal hypergraph Ramsey numbers have the conjectured tower height?”