{"paper":{"title":"Universality of the fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models converge to universal Gaussian limits in the high-temperature regime.","cross_cats":["math-ph","math.MP","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Hyunsuk Choo, Ji Oon Lee, Yoochan Han","submitted_at":"2026-05-07T23:59:32Z","abstract_excerpt":"We consider the fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio of spiked Wigner models in the high temperature/subcritical regime. We prove that the limiting laws of the fluctuations are Gaussian under suitable assumptions, and the result is universal in the sense that it does not depend on the distribution of the disorder or the prior except that the means and the variances of the limiting laws depend on a few parameters of the model. The proof is based on the multigraph expansion that provides a unified approach to analyze both mode"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the limiting laws of the fluctuations are Gaussian under suitable assumptions, and the result is universal in the sense that it does not depend on the distribution of the disorder or the prior except that the means and the variances of the limiting laws depend on a few parameters of the model.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The models operate in the high temperature/subcritical regime and satisfy suitable assumptions on the disorder and prior distributions that enable the multigraph expansion to yield Gaussian limits.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Fluctuations in free energy and log-likelihood ratio for generalized SK and spiked Wigner models are Gaussian and universal in the high-temperature regime.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models converge to universal Gaussian limits in the high-temperature regime.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5f744c403c4c8715084330af0cdb0e584639b659c24cf839dee2f8738efeeb79"},"source":{"id":"2605.07050","kind":"arxiv","version":2},"verdict":{"id":"fedce286-3a97-481d-94e6-6328d81d700d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-11T00:50:47.065480Z","strongest_claim":"We prove that the limiting laws of the fluctuations are Gaussian under suitable assumptions, and the result is universal in the sense that it does not depend on the distribution of the disorder or the prior except that the means and the variances of the limiting laws depend on a few parameters of the model.","one_line_summary":"Fluctuations in free energy and log-likelihood ratio for generalized SK and spiked Wigner models are Gaussian and universal in the high-temperature regime.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The models operate in the high temperature/subcritical regime and satisfy suitable assumptions on the disorder and prior distributions that enable the multigraph expansion to yield Gaussian limits.","pith_extraction_headline":"Fluctuations of the free energy in generalized Sherrington-Kirkpatrick models and the log likelihood ratio in spiked Wigner models converge to universal Gaussian limits in the high-temperature regime."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.07050/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T11:42:03.406218Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T06:37:25.963542Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T17:31:18.793324Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:09:47.681362Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"cb49646dcd862be7884db74f8709bb169e21d29f7a48664faacfc859c8d3023f"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"28ec3eb9b4a01352d40c420cdfbc5fa33fcc72789bd9656859bd72bc83bda6e0"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}