{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FK6CEOCXZK2CIJ7VLY5VIYQ4J5","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":"a97e13bd1c99380332d6706217a7d26fd6ff3e1e839407261c23289fbbc36395","cross_cats_sorted":["cond-mat.dis-nn","cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-08-28T08:00:55Z","title_canon_sha256":"8dc956bd16f6349f1120f647b01beb24eeb7706d072c3b665157e086e5c77954"},"schema_version":"1.0","source":{"id":"1008.4844","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4844","created_at":"2026-05-18T02:42:26Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4844v5","created_at":"2026-05-18T02:42:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4844","created_at":"2026-05-18T02:42:26Z"},{"alias_kind":"pith_short_12","alias_value":"FK6CEOCXZK2C","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FK6CEOCXZK2CIJ7V","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FK6CEOCX","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:407dce78dee6cdff7103ae644a2a1813277a69b7b715d2ccf078e70d43e46073","target":"graph","created_at":"2026-05-18T02:42:26Z","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":"These lecture notes focus on the mean field theory of spin glasses, with particular emphasis on the presence of a very large number of metastable states in these systems. This phenomenon, and some of its physical consequences, will be discussed in details for fully-connected models and for models defined on random lattices. This will be done using the replica and cavity methods.\n  These notes have been prepared for a course of the PhD program in Statistical Mechanics at SISSA, Trieste and at the University of Rome \"Sapienza\". Part of the material is reprinted from other lecture notes, and when","authors_text":"Francesco Zamponi","cross_cats":["cond-mat.dis-nn","cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-08-28T08:00:55Z","title":"Mean field theory of spin glasses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4844","kind":"arxiv","version":5},"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:aed569008056b4ba36264fba44dd73305e1719fc8f74f693127e662ea45537d6","target":"record","created_at":"2026-05-18T02:42:26Z","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":"a97e13bd1c99380332d6706217a7d26fd6ff3e1e839407261c23289fbbc36395","cross_cats_sorted":["cond-mat.dis-nn","cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-08-28T08:00:55Z","title_canon_sha256":"8dc956bd16f6349f1120f647b01beb24eeb7706d072c3b665157e086e5c77954"},"schema_version":"1.0","source":{"id":"1008.4844","kind":"arxiv","version":5}},"canonical_sha256":"2abc223857cab42427f55e3b54621c4f62eae893abad17f3a0b8c11c7185dc41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2abc223857cab42427f55e3b54621c4f62eae893abad17f3a0b8c11c7185dc41","first_computed_at":"2026-05-18T02:42:26.223031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:26.223031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"82DMJyywnpMSAwQWutkQMyQ3hSaH/+mFv0GlUxQdR8iK0s8oxRl/9sR81IHbeasYg/0IE4JT0riDXL3ORka+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:26.223767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4844","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aed569008056b4ba36264fba44dd73305e1719fc8f74f693127e662ea45537d6","sha256:407dce78dee6cdff7103ae644a2a1813277a69b7b715d2ccf078e70d43e46073"],"state_sha256":"c9361b36ccac15cbafcc82e5e92f74641087b4a788513e08650becf4480efede"}