{"id":"palomar/PALOMAR-2026-10-11-000006","url":"https://github.com/pmaronow/sk-mean-bias-palomar/tree/7601a9d5ade08066632bc68b9a615e163f2dd02c","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-11-000006-v1.json","repo":"https://github.com/pmaronow/sk-mean-bias-palomar","tags":["math.PR","cond-mat.dis-nn","msc:82B44","msc:60K35","msc:60G15","spin-glasses","free-energy","finite-size-effects","lean"],"score":0,"title":"Finite-size mean bias of the Sherrington-Kirkpatrick free energy","trust":"high","domain":"math.PR","source":"palomar","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"math.PR","summary":"Formalization of a fixed-temperature N^(-7/10) bound for the finite-size mean bias of the zero-field Sherrington-Kirkpatrick model with independent standard Gaussian couplings and the unnormalized partition function. For every beta > 1, a positive constant depending on beta bounds the nonnegative pressure gap for every integer N >= 2. The selected results also establish the thermodynamic limit for beta > 0, the corresponding free-energy-density and expected log-partition corrections, a positive exponent saving over 2/3, and a full-sequence little-o improvement. The independently readable…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-11","reactions":{},"formalized":true,"formalizes":[{"title":"An N^(-7/10) Bound for the Finite-Size Bias of the Sherrington-Kirkpatrick Free Energy","identifier":"paper/main.tex","relationship":"formalizes"}]}