Open Research Index

Full replica symmetry breaking in the Sherrington–Kirkpatrick model

P. M. Aronow, Patrick Lopatto

Palomar Registrypalomar/PALOMAR-2026-10-10-000001Oct 10, 2026math.PRscore 0

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,…

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-10-10-000001
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-10-000001/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-10-10-000001/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'