{"id":"palomar/PALOMAR-2026-10-10-000001","url":"https://github.com/pmaronow/frsb-palomar/tree/b3ff38e8bc8c057b8ee2addf0fa2428db32f106b","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-10-000001-v1.json","repo":"https://github.com/pmaronow/frsb-palomar","tags":["math.PR","math-ph","msc:82B44","msc:60G15","spin-glasses","replica-symmetry-breaking","probability","lean"],"score":0,"title":"Full replica symmetry breaking in the Sherrington–Kirkpatrick model","trust":"high","domain":"math.PR","source":"palomar","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"math.PR","summary":"Lean formalization of Patrick Lopatto's zero-field Sherrington–Kirkpatrick results. The selected claims are full interval support, a nonnegative smooth density with a terminal atom for every inverse temperature beta > 1, and quantitative inequalities for that actual atom. The independent Challenge defines the Parisi functional through concrete bounded-gradient weak PDE solutions, with terminal log cosh and coefficient beta squared divided by two. Solution identifies that definition with the constructed Parisi potential. The repository retains the supporting PDE, diffusion, covariance,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-10","reactions":{},"formalized":true,"formalizes":[{"title":"Full replica symmetry breaking in the Sherrington–Kirkpatrick model","identifier":"https://arxiv.org/abs/2607.11756v4","relationship":"formalizes"}]}