{"paper":{"title":"Potential Hessian Ascent III: Sampling the Sherrington--Kirkpatrick Model at Beta < 1/2","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure with negligible TVD error for all β < 1/2.","cross_cats":["cs.DS","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ewan Davies, Holden Lee, Jonathan Shi, Juspreet Singh Sandhu","submitted_at":"2026-05-05T13:06:26Z","abstract_excerpt":"We give a polynomial-time algorithm to sample from the Gibbs measure of the Sherrington-Kirkpatrick model with negligible total-variation distance (TVD) error up to inverse temperature $\\beta < 1/2$. Prior work obtained TVD error guarantees only up to $\\beta\\approx 0.295$, while results covering the entire replica-symmetric regime $\\beta < 1$ gave guarantees only in Wasserstein distance.\n  Our approach demonstrates that the same potential Hessian ascent previously developed for optimization also functions as a sampling algorithm by implementing algorithmic stochastic localization at high tempe"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We give a polynomial-time algorithm to sample from the Gibbs measure of the Sherrington--Kirkpatrick model with negligible total-variation distance (TVD) error up to inverse temperature β < 1/2.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The restricted log-Sobolev inequality holds on the time-T localized distribution and the free-probability argument controlling the diagonal sub-algebra of the Hessian yields an O(1) KL bound for the finite-time Hessian-ascent process at all β < 1/2.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A polynomial-time algorithm samples the SK model Gibbs measure with o(1) TVD error for β < 1/2 by combining potential Hessian ascent, stochastic localization, Jarzynski equality, and Glauber dynamics.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure with negligible TVD error for all β < 1/2.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0f232f803ea4f32f83dedea5d6f21eff3b55f12962bca7a8b1cd97e17dee8685"},"source":{"id":"2605.03718","kind":"arxiv","version":2},"verdict":{"id":"5dcc564b-2485-40f8-8594-4c767d8cee96","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T14:10:25.930237Z","strongest_claim":"We give a polynomial-time algorithm to sample from the Gibbs measure of the Sherrington--Kirkpatrick model with negligible total-variation distance (TVD) error up to inverse temperature β < 1/2.","one_line_summary":"A polynomial-time algorithm samples the SK model Gibbs measure with o(1) TVD error for β < 1/2 by combining potential Hessian ascent, stochastic localization, Jarzynski equality, and Glauber dynamics.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The restricted log-Sobolev inequality holds on the time-T localized distribution and the free-probability argument controlling the diagonal sub-algebra of the Hessian yields an O(1) KL bound for the finite-time Hessian-ascent process at all β < 1/2.","pith_extraction_headline":"Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure with negligible TVD error for all β < 1/2."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.03718/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-20T00:31:21.355617Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:04:57.235908Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7be0d9bfcc1ab339d33a25722cc1cfda313a0048d20301ab157554c2ac8e9ec6"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}