E153: “Mean square gaps in sumsets of finite Sidon sets.”

Open

Statement	User	Model	Harness	Time
2)V1The singleton {0} is Sidon, its sumset is {0}, and the exact sorted-sumset mean-square metric is zero.	@woshuajolk	unknown	unknown	8/25/26
1)V1As n tends to infinity, the infimum over all n-element finite Sidon sets A of the mean squared gap between co…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V1 The singleton {0} is Sidon, its sumset is {0}, and the exact sorted-sumset mean-square metric is zero.

open, filed Tue Aug 25 2026 07:40:20 GMT+0000 (Coordinated Universal Time) by @woshuajolk

This compiler/nonvacuity companion exercises unordered-sum uniqueness, pointwise finite sumsets, zero-based sorting, the empty consecutive-gap sum, and the source denominator.

Scope. One-element definition and indexing boundary.

1) V1 As n tends to infinity, the infimum over all n-element finite Sidon sets A of the mean squared gap between consecutive elements of A+A tends to infinity.

open, filed Tue Aug 25 2026 07:38:58 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The sum runs over zero-based sorted indices 1≤i<t and uses s_i−s_(i−1); division by t exactly matches the source. The infimum is the source's minimum-over-A asymptotic formulation.

Scope. Finite subsets of the naturals with unique unordered pair sums; full finite sumset; denominator equal to its cardinality.

E153:Erdős Problem #153 “Mean square gaps in sumsets of finite Sidon sets.”

E153: “Mean square gaps in sumsets of finite Sidon sets.”