{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FK6CEOCXZK2CIJ7VLY5VIYQ4J5","short_pith_number":"pith:FK6CEOCX","canonical_record":{"source":{"id":"1008.4844","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-08-28T08:00:55Z","cross_cats_sorted":["cond-mat.dis-nn","cs.CC"],"title_canon_sha256":"8dc956bd16f6349f1120f647b01beb24eeb7706d072c3b665157e086e5c77954","abstract_canon_sha256":"a97e13bd1c99380332d6706217a7d26fd6ff3e1e839407261c23289fbbc36395"},"schema_version":"1.0"},"canonical_sha256":"2abc223857cab42427f55e3b54621c4f62eae893abad17f3a0b8c11c7185dc41","source":{"kind":"arxiv","id":"1008.4844","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FK6CEOCXZK2CIJ7VLY5VIYQ4J5","target":"record","payload":{"canonical_record":{"source":{"id":"1008.4844","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-08-28T08:00:55Z","cross_cats_sorted":["cond-mat.dis-nn","cs.CC"],"title_canon_sha256":"8dc956bd16f6349f1120f647b01beb24eeb7706d072c3b665157e086e5c77954","abstract_canon_sha256":"a97e13bd1c99380332d6706217a7d26fd6ff3e1e839407261c23289fbbc36395"},"schema_version":"1.0"},"canonical_sha256":"2abc223857cab42427f55e3b54621c4f62eae893abad17f3a0b8c11c7185dc41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:26.223767Z","signature_b64":"82DMJyywnpMSAwQWutkQMyQ3hSaH/+mFv0GlUxQdR8iK0s8oxRl/9sR81IHbeasYg/0IE4JT0riDXL3ORka+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2abc223857cab42427f55e3b54621c4f62eae893abad17f3a0b8c11c7185dc41","last_reissued_at":"2026-05-18T02:42:26.223031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:26.223031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.4844","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PddofuQp71gFK0213AwU5l/9ApnOSViFz2LvaT/7U0naXA6TbOPavfJ+ehrG5lQGBEcFx/cgaykpnN06InUPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:40:43.550021Z"},"content_sha256":"aed569008056b4ba36264fba44dd73305e1719fc8f74f693127e662ea45537d6","schema_version":"1.0","event_id":"sha256:aed569008056b4ba36264fba44dd73305e1719fc8f74f693127e662ea45537d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FK6CEOCXZK2CIJ7VLY5VIYQ4J5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean field theory of spin glasses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.CC"],"primary_cat":"cond-mat.stat-mech","authors_text":"Francesco Zamponi","submitted_at":"2010-08-28T08:00:55Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4844","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8jVRPXeEgMpsB6rfocG3Mh6C/wyjSSQz52SwYvE0JkigcAlet39A9BVR0/BPmZQNBI0DEI8cIRRT9I/TMu4IBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:40:43.550765Z"},"content_sha256":"407dce78dee6cdff7103ae644a2a1813277a69b7b715d2ccf078e70d43e46073","schema_version":"1.0","event_id":"sha256:407dce78dee6cdff7103ae644a2a1813277a69b7b715d2ccf078e70d43e46073"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FK6CEOCXZK2CIJ7VLY5VIYQ4J5/bundle.json","state_url":"https://pith.science/pith/FK6CEOCXZK2CIJ7VLY5VIYQ4J5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FK6CEOCXZK2CIJ7VLY5VIYQ4J5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T08:40:43Z","links":{"resolver":"https://pith.science/pith/FK6CEOCXZK2CIJ7VLY5VIYQ4J5","bundle":"https://pith.science/pith/FK6CEOCXZK2CIJ7VLY5VIYQ4J5/bundle.json","state":"https://pith.science/pith/FK6CEOCXZK2CIJ7VLY5VIYQ4J5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FK6CEOCXZK2CIJ7VLY5VIYQ4J5/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ANHvQDsA633r60vx/2yhr0OJTEkgGxVuXf2Eo42U8VRMmkGnkKcS0E1FIb5Y9IF3EoGp+iKyiBUqBEvqBkhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:40:43.554751Z","bundle_sha256":"df64b8470620cd1f7916f84e757e777658c88af7c597eb444d68fc940b5e16c1"}}