Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 221. The Mézard–Parisi formula for diluted spin glasses
Family claims › Probability and statistical mechanics · lines 1491–1496
OpenAI@2026-10-07#rem:oai-221
Proves the Mézard–Parisi hierarchical cavity formula for Poisson-diluted even-arity Ising models satisfying the Panchenko–Talagrand factorization and positivity assumptions, with only first-moment integrability. The limiting free energy equals the infimum over finite-depth hierarchical trial laws. This includes the Viana–Bray model, symmetric diluted even-spin models, and weighted soft even- satisfiability.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
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