{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N7IHVOXLOD5FYLAB7MHZ52P3OM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bfe965028f708c916c8c0ee3623663cd16aff56f3ca46be87e5af945e535dfc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-29T02:21:44Z","title_canon_sha256":"e3e573431bff8439821bd9c175d3b55858eca96d72ee03cc0387f329affe2b28"},"schema_version":"1.0","source":{"id":"1901.10070","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10070","created_at":"2026-05-17T23:52:51Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10070v3","created_at":"2026-05-17T23:52:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10070","created_at":"2026-05-17T23:52:51Z"},{"alias_kind":"pith_short_12","alias_value":"N7IHVOXLOD5F","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N7IHVOXLOD5FYLAB","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N7IHVOXL","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:0f1d747de9ad37179ecb6b7bd3789e57085a9c7f20d3fb0b19c49272a9d43cc5","target":"graph","created_at":"2026-05-17T23:52:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present an elementary approach to the order of fluctuations for the free energy in the Sherrington-Kirkpatrick mean field spin glass model at and near the critical temperature. It is proved that at the critical temperature the variance of the free energy is of $O((\\log N)^2).$ In addition, we show that if one approaches the critical temperature from the low temperature regime at the rate $O(N^{-\\alpha})$ for some $\\alpha>0,$ then the variance is of $O((\\log N)^2+N^{1-\\alpha}).$","authors_text":"Wai-Kit Lam, Wei-Kuo Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-29T02:21:44Z","title":"Order of Fluctuations of the Free Energy in the SK Model at Critical Temperature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10070","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d4e812f4d4170a8dbb33ab767a4e74dbc64d030011df7418f5d7d69bf396486a","target":"record","created_at":"2026-05-17T23:52:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bfe965028f708c916c8c0ee3623663cd16aff56f3ca46be87e5af945e535dfc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-29T02:21:44Z","title_canon_sha256":"e3e573431bff8439821bd9c175d3b55858eca96d72ee03cc0387f329affe2b28"},"schema_version":"1.0","source":{"id":"1901.10070","kind":"arxiv","version":3}},"canonical_sha256":"6fd07abaeb70fa5c2c01fb0f9ee9fb733541220c4daffe3c3eea31c0e91d77ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fd07abaeb70fa5c2c01fb0f9ee9fb733541220c4daffe3c3eea31c0e91d77ef","first_computed_at":"2026-05-17T23:52:51.008588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:51.008588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rF+rXmbYnMQTL2dhQ8SSFAp34BPqp4qy3fYbaXDiIDEVtpOj5APuMj2SPVXBMVnIDz3RnIgp2083vK59n4jgAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:51.009344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.10070","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4e812f4d4170a8dbb33ab767a4e74dbc64d030011df7418f5d7d69bf396486a","sha256:0f1d747de9ad37179ecb6b7bd3789e57085a9c7f20d3fb0b19c49272a9d43cc5"],"state_sha256":"1c286ddfc6f396760c83a456969ba9fea852795fc3e27ee6be63da223158f693"}