{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:YAM4YZQ2PQCMFUYUEZ2EWE5GDD","short_pith_number":"pith:YAM4YZQ2","canonical_record":{"source":{"id":"0806.1709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-10T17:11:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ec4b9ccc4becd1ecec2cd5ef36b0d089a129de740a710164ed3280bba5b84bd1","abstract_canon_sha256":"92141beca39d09de8f1955ee6fbf5475869273353edbd8735367a73e13966961"},"schema_version":"1.0"},"canonical_sha256":"c019cc661a7c04c2d31426744b13a618c329f8d197d3d7ce60557bbbe85b609a","source":{"kind":"arxiv","id":"0806.1709","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.1709","created_at":"2026-07-04T15:34:57Z"},{"alias_kind":"arxiv_version","alias_value":"0806.1709v2","created_at":"2026-07-04T15:34:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.1709","created_at":"2026-07-04T15:34:57Z"},{"alias_kind":"pith_short_12","alias_value":"YAM4YZQ2PQCM","created_at":"2026-07-04T15:34:57Z"},{"alias_kind":"pith_short_16","alias_value":"YAM4YZQ2PQCMFUYU","created_at":"2026-07-04T15:34:57Z"},{"alias_kind":"pith_short_8","alias_value":"YAM4YZQ2","created_at":"2026-07-04T15:34:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:YAM4YZQ2PQCMFUYUEZ2EWE5GDD","target":"record","payload":{"canonical_record":{"source":{"id":"0806.1709","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-10T17:11:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ec4b9ccc4becd1ecec2cd5ef36b0d089a129de740a710164ed3280bba5b84bd1","abstract_canon_sha256":"92141beca39d09de8f1955ee6fbf5475869273353edbd8735367a73e13966961"},"schema_version":"1.0"},"canonical_sha256":"c019cc661a7c04c2d31426744b13a618c329f8d197d3d7ce60557bbbe85b609a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:34:57.665532Z","signature_b64":"S+Nq/ZsmJkTC9IDo5VVFZcmmaq81O4ptdrPvsYkPAso+sQMF+KyliJGsldk0yDY3K+e7OyEkeP+FbDgbfK6nDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c019cc661a7c04c2d31426744b13a618c329f8d197d3d7ce60557bbbe85b609a","last_reissued_at":"2026-07-04T15:34:57.665096Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:34:57.665096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0806.1709","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:34:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wuVJPx5kKTwY+szeJU2G6aB6nHsBi8zKHLYqp1oW2QYvHWvojF3YZePv45+2jMe/6YVi9ZKkLMKJIqXsCuAeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:48:46.135978Z"},"content_sha256":"bfa5781fd361b5706da9502aeaca6be97f7fd9b55a2ab57dd14e138733ee7e87","schema_version":"1.0","event_id":"sha256:bfa5781fd361b5706da9502aeaca6be97f7fd9b55a2ab57dd14e138733ee7e87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:YAM4YZQ2PQCMFUYUEZ2EWE5GDD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Thermodynamic Limit of Quantum Coulomb Systems. Part II. Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Christian Hainzl, Jan Philip Solovej, Mathieu Lewin","submitted_at":"2008-06-10T17:11:08Z","abstract_excerpt":"In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume.\n  The first system is the crystal for which the nuclei are classical particles arranged periodically in space and only the electrons are quantum particles. We recover and generalize a previous result of Fefferman. In the second example, both the nuclei and the electrons are quantum particles, submitted to a periodic magnetic field. We thereby extend a seminal result of Lieb and Lebowi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1709","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0806.1709/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:34:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oD+4Mm/EXt0LXiytOLjMstt8OEWJY7kJR16fRQb0I+OX/p8pOpTxHIrw1FEJtVxuhA3fFObyqaNERMkz1BGuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:48:46.136364Z"},"content_sha256":"b341be73039a5e1480ddd33e3f05a2a909471568ffbaec4b7fb68b228e21e31a","schema_version":"1.0","event_id":"sha256:b341be73039a5e1480ddd33e3f05a2a909471568ffbaec4b7fb68b228e21e31a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YAM4YZQ2PQCMFUYUEZ2EWE5GDD/bundle.json","state_url":"https://pith.science/pith/YAM4YZQ2PQCMFUYUEZ2EWE5GDD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YAM4YZQ2PQCMFUYUEZ2EWE5GDD/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":"2026-08-04T07:48:46Z","links":{"resolver":"https://pith.science/pith/YAM4YZQ2PQCMFUYUEZ2EWE5GDD","bundle":"https://pith.science/pith/YAM4YZQ2PQCMFUYUEZ2EWE5GDD/bundle.json","state":"https://pith.science/pith/YAM4YZQ2PQCMFUYUEZ2EWE5GDD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YAM4YZQ2PQCMFUYUEZ2EWE5GDD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:YAM4YZQ2PQCMFUYUEZ2EWE5GDD","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":"92141beca39d09de8f1955ee6fbf5475869273353edbd8735367a73e13966961","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-10T17:11:08Z","title_canon_sha256":"ec4b9ccc4becd1ecec2cd5ef36b0d089a129de740a710164ed3280bba5b84bd1"},"schema_version":"1.0","source":{"id":"0806.1709","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.1709","created_at":"2026-07-04T15:34:57Z"},{"alias_kind":"arxiv_version","alias_value":"0806.1709v2","created_at":"2026-07-04T15:34:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.1709","created_at":"2026-07-04T15:34:57Z"},{"alias_kind":"pith_short_12","alias_value":"YAM4YZQ2PQCM","created_at":"2026-07-04T15:34:57Z"},{"alias_kind":"pith_short_16","alias_value":"YAM4YZQ2PQCMFUYU","created_at":"2026-07-04T15:34:57Z"},{"alias_kind":"pith_short_8","alias_value":"YAM4YZQ2","created_at":"2026-07-04T15:34:57Z"}],"graph_snapshots":[{"event_id":"sha256:b341be73039a5e1480ddd33e3f05a2a909471568ffbaec4b7fb68b228e21e31a","target":"graph","created_at":"2026-07-04T15:34:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0806.1709/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume.\n  The first system is the crystal for which the nuclei are classical particles arranged periodically in space and only the electrons are quantum particles. We recover and generalize a previous result of Fefferman. In the second example, both the nuclei and the electrons are quantum particles, submitted to a periodic magnetic field. We thereby extend a seminal result of Lieb and Lebowi","authors_text":"Christian Hainzl, Jan Philip Solovej, Mathieu Lewin","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-10T17:11:08Z","title":"The Thermodynamic Limit of Quantum Coulomb Systems. Part II. Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1709","kind":"arxiv","version":2},"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:bfa5781fd361b5706da9502aeaca6be97f7fd9b55a2ab57dd14e138733ee7e87","target":"record","created_at":"2026-07-04T15:34:57Z","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":"92141beca39d09de8f1955ee6fbf5475869273353edbd8735367a73e13966961","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-10T17:11:08Z","title_canon_sha256":"ec4b9ccc4becd1ecec2cd5ef36b0d089a129de740a710164ed3280bba5b84bd1"},"schema_version":"1.0","source":{"id":"0806.1709","kind":"arxiv","version":2}},"canonical_sha256":"c019cc661a7c04c2d31426744b13a618c329f8d197d3d7ce60557bbbe85b609a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c019cc661a7c04c2d31426744b13a618c329f8d197d3d7ce60557bbbe85b609a","first_computed_at":"2026-07-04T15:34:57.665096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:34:57.665096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S+Nq/ZsmJkTC9IDo5VVFZcmmaq81O4ptdrPvsYkPAso+sQMF+KyliJGsldk0yDY3K+e7OyEkeP+FbDgbfK6nDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:34:57.665532Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.1709","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfa5781fd361b5706da9502aeaca6be97f7fd9b55a2ab57dd14e138733ee7e87","sha256:b341be73039a5e1480ddd33e3f05a2a909471568ffbaec4b7fb68b228e21e31a"],"state_sha256":"4a008533bbac8f1b8b751cdd3debaa2cce9c135ece77a20460b2320ce942e04d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"er4A+R6TDZ8qqDViDQXvWO3TXZZMJ4NSzcysnT5wWhDFJyn9nvbbpJsU1YaNvOkbqZjNMSYcqBuirVhqqcb2Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T07:48:46.139141Z","bundle_sha256":"28fff638211378bfd0b188a4ef9faab46ae7d2ec702b60f26762322b4a33da3a"}}