{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GLSNYNBA2OAB47MPMKTSGBWMTV","short_pith_number":"pith:GLSNYNBA","canonical_record":{"source":{"id":"1409.1182","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-03T18:04:17Z","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","math.AP","math.MP"],"title_canon_sha256":"b5f90b7f8cfff07d3acf5da12d577629a0b7e91cfbbef7fd301f9750b9bb374b","abstract_canon_sha256":"4a2d3fe8716a355aae6e6c8adf03b94f5b6b99fe86bdc41debcd67265cb73460"},"schema_version":"1.0"},"canonical_sha256":"32e4dc3420d3801e7d8f62a72306cc9d6a4e50e999876c09ec9be37b144d81d2","source":{"kind":"arxiv","id":"1409.1182","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1182","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1182v4","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1182","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"GLSNYNBA2OAB","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GLSNYNBA2OAB47MP","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GLSNYNBA","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GLSNYNBA2OAB47MPMKTSGBWMTV","target":"record","payload":{"canonical_record":{"source":{"id":"1409.1182","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-03T18:04:17Z","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","math.AP","math.MP"],"title_canon_sha256":"b5f90b7f8cfff07d3acf5da12d577629a0b7e91cfbbef7fd301f9750b9bb374b","abstract_canon_sha256":"4a2d3fe8716a355aae6e6c8adf03b94f5b6b99fe86bdc41debcd67265cb73460"},"schema_version":"1.0"},"canonical_sha256":"32e4dc3420d3801e7d8f62a72306cc9d6a4e50e999876c09ec9be37b144d81d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:07.736352Z","signature_b64":"pSy3+VuJdd+FuBcWM2uSBRE3Re5zyucufIwjpCqSJgL1/76GjWLVgsXSNwZKdBnDim1Fd8wnTOPhPBuTIAttAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32e4dc3420d3801e7d8f62a72306cc9d6a4e50e999876c09ec9be37b144d81d2","last_reissued_at":"2026-05-18T02:27:07.735547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:07.735547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.1182","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V6uJWFE6OIZpTSZpHk3h4Z6WXbt+vZorTmdEt8f+DYFtn4J09oxKs9sScylt9+YxjevdUisp4I7NWyj3Fr1NBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:52:30.067962Z"},"content_sha256":"330a673b4165e2cd20638994a312b2229dfaf8b187a24f67722521223eced575","schema_version":"1.0","event_id":"sha256:330a673b4165e2cd20638994a312b2229dfaf8b187a24f67722521223eced575"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GLSNYNBA2OAB47MPMKTSGBWMTV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Th\\'eor\\`emes de de Finetti, limites de champ moyen et condensation de Bose-Einstein","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","cond-mat.stat-mech","math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Nicolas Rougerie (LPMMC)","submitted_at":"2014-09-03T18:04:17Z","abstract_excerpt":"These lecture notes treat the mean-field approximation for equilibrium states of N body systems in classical and quantum statistical mechanics. A general strategy to justify effective models based on assumptions  of statistical independence of the particles is in presented in detail. The main tools are a structure theorems of de Finetti that describe large N limits of states accessible to the systems in question, exploiting the indistinguishablity of particles. The focus is on quantum aspects, particularly the mean-field approximation for the ground state of a large system of bosons, in connec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1182","kind":"arxiv","version":4},"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":"2026-05-18T02:27:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4f1Yd7dZrAzG9qEJc0MJvSrJqbI35ynUDzyJoyxlY04Mnps4SDyfBaowDlu8QA2bRyJEAKPGsORXvPnESBlPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:52:30.068359Z"},"content_sha256":"0798c4363de8975e5bd15c20b12d07711e63e3eeff3e54c7e71bf332952a5577","schema_version":"1.0","event_id":"sha256:0798c4363de8975e5bd15c20b12d07711e63e3eeff3e54c7e71bf332952a5577"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GLSNYNBA2OAB47MPMKTSGBWMTV/bundle.json","state_url":"https://pith.science/pith/GLSNYNBA2OAB47MPMKTSGBWMTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GLSNYNBA2OAB47MPMKTSGBWMTV/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":"2026-06-28T21:52:30Z","links":{"resolver":"https://pith.science/pith/GLSNYNBA2OAB47MPMKTSGBWMTV","bundle":"https://pith.science/pith/GLSNYNBA2OAB47MPMKTSGBWMTV/bundle.json","state":"https://pith.science/pith/GLSNYNBA2OAB47MPMKTSGBWMTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GLSNYNBA2OAB47MPMKTSGBWMTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GLSNYNBA2OAB47MPMKTSGBWMTV","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":"4a2d3fe8716a355aae6e6c8adf03b94f5b6b99fe86bdc41debcd67265cb73460","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-03T18:04:17Z","title_canon_sha256":"b5f90b7f8cfff07d3acf5da12d577629a0b7e91cfbbef7fd301f9750b9bb374b"},"schema_version":"1.0","source":{"id":"1409.1182","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1182","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1182v4","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1182","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"GLSNYNBA2OAB","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GLSNYNBA2OAB47MP","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GLSNYNBA","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:0798c4363de8975e5bd15c20b12d07711e63e3eeff3e54c7e71bf332952a5577","target":"graph","created_at":"2026-05-18T02:27:07Z","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 treat the mean-field approximation for equilibrium states of N body systems in classical and quantum statistical mechanics. A general strategy to justify effective models based on assumptions  of statistical independence of the particles is in presented in detail. The main tools are a structure theorems of de Finetti that describe large N limits of states accessible to the systems in question, exploiting the indistinguishablity of particles. The focus is on quantum aspects, particularly the mean-field approximation for the ground state of a large system of bosons, in connec","authors_text":"Nicolas Rougerie (LPMMC)","cross_cats":["cond-mat.quant-gas","cond-mat.stat-mech","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-03T18:04:17Z","title":"Th\\'eor\\`emes de de Finetti, limites de champ moyen et condensation de Bose-Einstein"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1182","kind":"arxiv","version":4},"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":"sha256:330a673b4165e2cd20638994a312b2229dfaf8b187a24f67722521223eced575","target":"record","created_at":"2026-05-18T02:27:07Z","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":"4a2d3fe8716a355aae6e6c8adf03b94f5b6b99fe86bdc41debcd67265cb73460","cross_cats_sorted":["cond-mat.quant-gas","cond-mat.stat-mech","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-09-03T18:04:17Z","title_canon_sha256":"b5f90b7f8cfff07d3acf5da12d577629a0b7e91cfbbef7fd301f9750b9bb374b"},"schema_version":"1.0","source":{"id":"1409.1182","kind":"arxiv","version":4}},"canonical_sha256":"32e4dc3420d3801e7d8f62a72306cc9d6a4e50e999876c09ec9be37b144d81d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32e4dc3420d3801e7d8f62a72306cc9d6a4e50e999876c09ec9be37b144d81d2","first_computed_at":"2026-05-18T02:27:07.735547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:07.735547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pSy3+VuJdd+FuBcWM2uSBRE3Re5zyucufIwjpCqSJgL1/76GjWLVgsXSNwZKdBnDim1Fd8wnTOPhPBuTIAttAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:07.736352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1182","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:330a673b4165e2cd20638994a312b2229dfaf8b187a24f67722521223eced575","sha256:0798c4363de8975e5bd15c20b12d07711e63e3eeff3e54c7e71bf332952a5577"],"state_sha256":"625ba11fd696d303f074dfc20282aba4c6d10f8c1b60540403ec361852bb987a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvrCoNTFT7DpIABNfg6WwTlYIXafNX+HDWNp5iubyigfTjX60ELzBD7/d3Go6OBdcsu/UBFLtmX2UDzC6g3WDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T21:52:30.070271Z","bundle_sha256":"87d40593944d0ccf3f998f4f5305e170115c2a7688c18d1fbf3cf23117ae3869"}}