{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:ZOD5MJH2SZKL373QMOYZVANEKO","short_pith_number":"pith:ZOD5MJH2","canonical_record":{"source":{"id":"cond-mat/0504132","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-04-06T10:04:32Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"9676dee71f3a44bfa3b6cbea61a56d01ce0cb1b7fa2340253a67303b0484bbd1","abstract_canon_sha256":"5bba38476273c6574f5a0f9ea51f53f49549e5aee4fcd98fb54dbc42afbf7606"},"schema_version":"1.0"},"canonical_sha256":"cb87d624fa9654bdff7063b19a81a4539ba2aa6bd8a2d42c75dbe3ef7752b329","source":{"kind":"arxiv","id":"cond-mat/0504132","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0504132","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0504132v1","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0504132","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZOD5MJH2SZKL","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZOD5MJH2SZKL373Q","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZOD5MJH2","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:ZOD5MJH2SZKL373QMOYZVANEKO","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0504132","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-04-06T10:04:32Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"9676dee71f3a44bfa3b6cbea61a56d01ce0cb1b7fa2340253a67303b0484bbd1","abstract_canon_sha256":"5bba38476273c6574f5a0f9ea51f53f49549e5aee4fcd98fb54dbc42afbf7606"},"schema_version":"1.0"},"canonical_sha256":"cb87d624fa9654bdff7063b19a81a4539ba2aa6bd8a2d42c75dbe3ef7752b329","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:53.341609Z","signature_b64":"orkN4E/GQADvv38nuVfgxWVK7I/xiqVDg5S1qTKICPeKCiVx9F40g9Jp4aSNRRj279VHBh4eKXSb29tkSiQbBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb87d624fa9654bdff7063b19a81a4539ba2aa6bd8a2d42c75dbe3ef7752b329","last_reissued_at":"2026-05-18T01:39:53.341127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:53.341127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0504132","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qRLJmR2AJpHp+CYrGjXRWPy+NNh7hAk4N1FPkaf8SuxBKWWhBKLKVbLaFYoJ7CqxE/PeB3qx1qPwblJi95G7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T04:10:29.536738Z"},"content_sha256":"525a3c67adcbfe2515cad23897d208056c7fe267bf7adeaaeef92d285fb6e18e","schema_version":"1.0","event_id":"sha256:525a3c67adcbfe2515cad23897d208056c7fe267bf7adeaaeef92d285fb6e18e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:ZOD5MJH2SZKL373QMOYZVANEKO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermodynamic origin of order parameters in mean-field models of spin glasses","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"L. Zdeborova, V. Janis","submitted_at":"2005-04-06T10:04:32Z","abstract_excerpt":"We analyze thermodynamic behavior of general $n$-component mean-field spin glass models in order to identify origin of the hierarchical structure of the order parameters from the replica-symmetry breaking solution. We derive a configurationally dependent free energy with local magnetizations and averaged local susceptibilities as order parameters. On an example of the replicated Ising spin glass we demonstrate that the hierarchy of order parameters in mean-field models results from the structure of inter-replica susceptibilities. These susceptibilities serve for lifting the degeneracy due to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0504132","kind":"arxiv","version":1},"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":"2026-05-18T01:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+kzrs/aoDq7TpyBHQ5qPEHAxRxa2AXLZ5JpIiIr/ZvZGAO7Dhr34HBH/9RB5HMQ46TKVDz7vxxYPi4SLwz/lBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T04:10:29.537082Z"},"content_sha256":"c5f53d5f3b9754aa08366dacd25646b1eb4f6dd404cc17558ccf245be1abfe3d","schema_version":"1.0","event_id":"sha256:c5f53d5f3b9754aa08366dacd25646b1eb4f6dd404cc17558ccf245be1abfe3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZOD5MJH2SZKL373QMOYZVANEKO/bundle.json","state_url":"https://pith.science/pith/ZOD5MJH2SZKL373QMOYZVANEKO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZOD5MJH2SZKL373QMOYZVANEKO/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":"2026-06-22T04:10:29Z","links":{"resolver":"https://pith.science/pith/ZOD5MJH2SZKL373QMOYZVANEKO","bundle":"https://pith.science/pith/ZOD5MJH2SZKL373QMOYZVANEKO/bundle.json","state":"https://pith.science/pith/ZOD5MJH2SZKL373QMOYZVANEKO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZOD5MJH2SZKL373QMOYZVANEKO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:ZOD5MJH2SZKL373QMOYZVANEKO","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":"5bba38476273c6574f5a0f9ea51f53f49549e5aee4fcd98fb54dbc42afbf7606","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-04-06T10:04:32Z","title_canon_sha256":"9676dee71f3a44bfa3b6cbea61a56d01ce0cb1b7fa2340253a67303b0484bbd1"},"schema_version":"1.0","source":{"id":"cond-mat/0504132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0504132","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0504132v1","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0504132","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZOD5MJH2SZKL","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZOD5MJH2SZKL373Q","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZOD5MJH2","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:c5f53d5f3b9754aa08366dacd25646b1eb4f6dd404cc17558ccf245be1abfe3d","target":"graph","created_at":"2026-05-18T01:39:53Z","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 analyze thermodynamic behavior of general $n$-component mean-field spin glass models in order to identify origin of the hierarchical structure of the order parameters from the replica-symmetry breaking solution. We derive a configurationally dependent free energy with local magnetizations and averaged local susceptibilities as order parameters. On an example of the replicated Ising spin glass we demonstrate that the hierarchy of order parameters in mean-field models results from the structure of inter-replica susceptibilities. These susceptibilities serve for lifting the degeneracy due to t","authors_text":"L. Zdeborova, V. Janis","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-04-06T10:04:32Z","title":"Thermodynamic origin of order parameters in mean-field models of spin glasses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0504132","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":"sha256:525a3c67adcbfe2515cad23897d208056c7fe267bf7adeaaeef92d285fb6e18e","target":"record","created_at":"2026-05-18T01:39:53Z","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":"5bba38476273c6574f5a0f9ea51f53f49549e5aee4fcd98fb54dbc42afbf7606","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2005-04-06T10:04:32Z","title_canon_sha256":"9676dee71f3a44bfa3b6cbea61a56d01ce0cb1b7fa2340253a67303b0484bbd1"},"schema_version":"1.0","source":{"id":"cond-mat/0504132","kind":"arxiv","version":1}},"canonical_sha256":"cb87d624fa9654bdff7063b19a81a4539ba2aa6bd8a2d42c75dbe3ef7752b329","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb87d624fa9654bdff7063b19a81a4539ba2aa6bd8a2d42c75dbe3ef7752b329","first_computed_at":"2026-05-18T01:39:53.341127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:53.341127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"orkN4E/GQADvv38nuVfgxWVK7I/xiqVDg5S1qTKICPeKCiVx9F40g9Jp4aSNRRj279VHBh4eKXSb29tkSiQbBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:53.341609Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0504132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:525a3c67adcbfe2515cad23897d208056c7fe267bf7adeaaeef92d285fb6e18e","sha256:c5f53d5f3b9754aa08366dacd25646b1eb4f6dd404cc17558ccf245be1abfe3d"],"state_sha256":"85711efe352c61fb4da87423b3da6edd525a61eb078bb77557d2a71a148542ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pCzvZMA2mvoodJF6wek7nvD9VNEusOhrowBh/3VXyaDFND7f4GT1kxf30R9BZszB/1QaeiSP1gOJ2p0M3RiaAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T04:10:29.539076Z","bundle_sha256":"74128a0dd010623cb2fb900becdc55094a93e4488debc15e6ff067315d637dea"}}