Problem detail · source-aware
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Nathanson asked which subsets of $\mathbb{N}$ can occur as product intersection sets of a family of semigroup subsets, for arbitrary and for decreasing families (his Problems 10 and 11). Both are solved by complete classifications.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
"Both classifications were autonomously discovered and formally verified in Lean by Aristotle." The appendix documents the prompts: Aristotle was asked to characterize the two cases separately, then combine them; it even adopted a stronger definition than the source paper's and the Lean code verifies the equivalence explicitly.
Provider: Harmonic · Prompt public: unknown · Independence: unknown
Discovered and kernel-checked in Lean by the same system; the human authors audited the informal-to-formal correspondence. Tier: Aristotle wrote both proof and formal statements (and at one point adopted a stronger definition than the source paper's, caught by the authors) - exactly the failure mode an independent statement audit exists for, and none has happened.
Correctness: supported · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.