E538: “Does the normalized Erdős 538 reciprocal extremum have a positive limit?”

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Statement	User	Model	Harness	Time
2)V2For every representation cap r and finite interval {1,…,N}, an admissible finite set attains the exact maximu…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every fixed r≥2, does the exact maximum reciprocal mass over sets with at most r representations m=pa, no…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 For every representation cap r and finite interval {1,…,N}, an admissible finite set attains the exact maximum reciprocal mass.

kernel-checked, filed Tue Aug 25 2026 05:53:08 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. All natural r and N; the same admissibility predicate and exact sSup used by the root.

1) V1 For every fixed r≥2, does the exact maximum reciprocal mass over sets with at most r representations m=pa, normalized by log log N/log N, tend to a positive constant?

open, filed Tue Aug 25 2026 05:52:42 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Formal written first from the fixed RHS in formal-conjectures. `representations` counts ordered pairs (p,a) with p prime and a∈A; `Admissible` includes A⊆{1,…,N} and the cap for every m; `maxMass` is the exact finite extremum; the normalized Tendsto proposition is the explicit sharp-constant question. This is labelled as a refinement rather than silently equated with the source's open-ended wording. One scope is used in formal, prose, and DAG.

Scope. Every fixed natural r≥2; exact extrema over finite A⊆{1,…,N}; limit as N tends to infinity.

E538:Erdős Problem #538 “Does the normalized Erdős 538 reciprocal extremum have a positive limit?”

E538: “Does the normalized Erdős 538 reciprocal extremum have a positive limit?”