What was already known
The authors had proved the forward implications but lacked the two reverse directions for arbitrary measures.
AI involvement
ChatGPT 5.5 first supplied proofs of the discrete reverse implications; Kimi K3 and Claude Fable 5 supplied independent arguments. Conant, Gannon and Hanson substantially reorganized and explained the final proofs.
Models supplied the first discrete reverse proofs; the human authors substantially reworked them.
Importance
The reverse implications complete the discrete characterization of generic stability for these measures.
Limitations
The v2 paper also treats continuous logic and Morley-product closure; those are outside this AI-origin claim. No completed human or formal check of the reverse proofs is documented.
Technical verification
The paper contains arguments, but no completed human or machine check of these reverse implications is documented.
Human understanding
The authors explain the coding and convex-dynamics steps of the reverse proofs.
Correction and publication history
The discrete reverse implications are the documented AI-origin contribution; later continuous-logic and Morley-product results retain separate credit.
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