{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BXQEM4VZBXWD44AIRYIWJ3WSGD","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":"c739cd5d8474440c76c0888a7d0ace557cdba9fa4525aff647088419bc6ab78d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-03-26T20:48:20Z","title_canon_sha256":"03e2d81fca6ec43ec63d70cb8ab1a05b0e5f07a0bf8488f53871978d1fb1e231"},"schema_version":"1.0","source":{"id":"1003.5226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5226","created_at":"2026-05-18T02:08:16Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5226v1","created_at":"2026-05-18T02:08:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5226","created_at":"2026-05-18T02:08:16Z"},{"alias_kind":"pith_short_12","alias_value":"BXQEM4VZBXWD","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BXQEM4VZBXWD44AI","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BXQEM4VZ","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:a604966b744977147556ce39e1bd78b9c84f1fe971970056275de6460885f2e4","target":"graph","created_at":"2026-05-18T02:08:16Z","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":"During the last years, through the combined effort of the insight, coming from physical intuition and computer simulation, and the exploitation of rigorous mathematical methods, the main features of the mean field Sherrington-Kirkpatrick spin glass model have been firmly established. In particular, it has been possible to prove the existence and uniqueness of the infinite volume limit for the free energy, and its Parisi expression, in terms of a variational principle, involving a functional order parameter. Even the expected property of ultrametricity, for the infinite volume states, seems to ","authors_text":"Adriano Barra, Aldo Di Biasio, Francesco Guerra","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-03-26T20:48:20Z","title":"Replica symmetry breaking in mean field spin glasses trough Hamilton-Jacobi technique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5226","kind":"arxiv","version":1},"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":"sha256:394c3738f67b63bcc861068cfb9105b9feb84e7493c7d355c23d135d5636ca70","target":"record","created_at":"2026-05-18T02:08:16Z","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":"c739cd5d8474440c76c0888a7d0ace557cdba9fa4525aff647088419bc6ab78d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-03-26T20:48:20Z","title_canon_sha256":"03e2d81fca6ec43ec63d70cb8ab1a05b0e5f07a0bf8488f53871978d1fb1e231"},"schema_version":"1.0","source":{"id":"1003.5226","kind":"arxiv","version":1}},"canonical_sha256":"0de04672b90dec3e70088e1164eed230fdc73cb46b29ddf9b6e69cce24996e0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0de04672b90dec3e70088e1164eed230fdc73cb46b29ddf9b6e69cce24996e0e","first_computed_at":"2026-05-18T02:08:16.589273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:16.589273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4B7Hc53nHCr2bWfsD3Y1lv7i0dVArD2dRZ9gzBXsEJOYNEI8RZvzdVcFgUXn4kmYFS6WzZPmNPji4L86iMaCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:16.589923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:394c3738f67b63bcc861068cfb9105b9feb84e7493c7d355c23d135d5636ca70","sha256:a604966b744977147556ce39e1bd78b9c84f1fe971970056275de6460885f2e4"],"state_sha256":"6dddd1b98d427d2a6937d31f68a3947f6f3231b1b9b624014cfaffe16e3660b4"}