{"id":"palomar/PALOMAR-2026-10-11-000017","url":"https://github.com/pmaronow/arbitrary-rsb-palomar/tree/5162e2d15b440ce46fd322f20eb429468d601948","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-11-000017-v1.json","repo":"https://github.com/pmaronow/arbitrary-rsb-palomar","tags":["math.PR","math-ph","msc:60K35","msc:82B44","spin-glasses","replica-symmetry-breaking","lean-formalization"],"score":0,"title":"Replica symmetry breaking at arbitrary depth","trust":"high","domain":"math.PR","source":"palomar","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"math.PR","summary":"A Lean formalization of open phases with every prescribed finite replica symmetry breaking depth in mixed even-spin Ising models at zero external field and positive temperature. The first selected result constructs strictly increasing even degrees beginning at four and a nonempty open set of positive effective covariance coefficients, with an optimizing probability measure having exactly k+1 support points. The independent statement uses concrete Gaussian Cole–Hopf recursions and comparison against all finite schemes at every competing depth. The substantive development constructs minimizers…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-11","reactions":{},"formalized":true,"formalizes":[{"title":"Replica symmetry breaking at arbitrary depth","identifier":"https://arxiv.org/abs/2609.05317","relationship":"formalizes"}]}