{"id":"palomar/PALOMAR-2026-10-12-000002","url":"https://github.com/pmaronow/aging-palomar/tree/d3f09f56462be6f73eb20733cb7963410409fa06","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-12-000002-v1.json","repo":"https://github.com/pmaronow/aging-palomar","tags":["math.PR","math.AP","msc:60H10","msc:82D30","msc:60G15","spin-glasses","stochastic-dynamics","lean-formalization"],"score":0,"title":"Aging in Spherical Spin Glass Dynamics","trust":"high","domain":"math.PR","source":"palomar","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"math.PR","summary":"Lean formalization of the spherical Gaussian spin-glass dynamics and its positive-semidefinite Cugliandolo--Kurchan limit, including the physical variational response, entropy and Fisher estimates, stationary translated clusters, general-spin selection and aging bounds, and stationary relaxation. Theorem 11.4 covers every integer p >= 3 and beta > 0. The cubic product inequality includes beta = beta_d; strictly positive Fisher-cost conclusions require beta > beta_d. The root Challenge retains the original complete-conclusions theorem with the five principal theorem groups and all-spin…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-12","reactions":{},"formalized":true,"formalizes":[{"title":"Aging in Spherical Spin Glass Dynamics","identifier":"","relationship":"formalizes"}]}