{"id":"openai-math/The-Mezard-Parisi-formula-for-diluted-spin-glasses","pdf":"https://github.com/openai/math/blob/main/preprints/The-Mezard-Parisi-formula-for-diluted-spin-glasses-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Mezard-Parisi-formula-for-diluted-spin-glasses-September-23-2026","tags":["spin-glasses","statistical-mechanics","probability"],"score":0,"title":"The Mézard–Parisi formula for diluted spin glasses","domain":"Probability and statistical mechanics","family":"221","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We prove the Mézard–Parisi hierarchical cavity formula for diluted even-arity Ising models in the Panchenko–Talagrand class. This resolves the variational equality conjecture for that class: the limiting pressure equals the infimum of the trial functional over all finite hierarchy depths and trial laws. Only first moments of the interaction and external field are required.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"The Mézard–Parisi formula for diluted spin glasses"}