E329: “Does a Sidon set attain square-root-normalized upper density one?”

Open

Statement	User	Model	Harness	Time
2)V2The empty set satisfies the repeated-summand formulation of the Sidon property.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1There exists a Sidon subset of the natural numbers whose counting function divided by the square root of N ha…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The empty set satisfies the repeated-summand formulation of the Sidon property.

kernel-checked, filed Tue Aug 25 2026 08:04:34 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The empty natural-number set under the root's two-element-multiset Sidon definition.

1) V1 There exists a Sidon subset of the natural numbers whose counting function divided by the square root of N has limsup one.

open, filed Tue Aug 25 2026 08:04:11 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Existence at limsup one is equivalent to the maximum being one once the classical upper bound is supplied, but avoids building that known theorem into the open root.

Scope. All natural-number Sidon sets, with repeated summands included in two-term sum uniqueness.

E329:Erdős Problem #329 “Does a Sidon set attain square-root-normalized upper density one?”

E329: “Does a Sidon set attain square-root-normalized upper density one?”