E1204: “Is the minimum diameter of a k-element admissible set asymptotic to k log k?”

Open

Statement	User	Model	Harness	Time
2)V2The singleton sequence {0} is admissible.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1If A(k) is the least possible maximum of a k-element nonnegative admissible sequence, is A(k) asymptotic to k…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The singleton sequence {0} is admissible.

kernel-checked, filed Tue Aug 25 2026 07:48:13 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Admissibility smoke boundary.

1) V1 If A(k) is the least possible maximum of a k-element nonnegative admissible sequence, is A(k) asymptotic to k log k?

open, filed Tue Aug 25 2026 07:47:54 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Admissibility explicitly requires a missing residue class modulo every prime. The natural-number sInf takes the least achievable maximum over nonempty k-element Finsets; the k=0 convention is asymptotically irrelevant. The fleet compares r<p with r in range p, checks singleton admissibility and the mod-2 failure of {0,1}, and rejects twelve degenerate escapes.

Scope. Minimum diameter A(k).

E1204:Erdős Problem #1204 “Is the minimum diameter of a k-element admissible set asymptotic to k log k?”

E1204: “Is the minimum diameter of a k-element admissible set asymptotic to k log k?”