{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:YCAO2GXPQRICWOYFJHFNXFXUYO","short_pith_number":"pith:YCAO2GXP","canonical_record":{"source":{"id":"2109.15301","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2021-09-30T17:47:22Z","cross_cats_sorted":["hep-ph","nucl-ex"],"title_canon_sha256":"4f78374c2be52a52296108858412756490f1bfd02e16a4d4cea406f2abd4161e","abstract_canon_sha256":"b910e8fd4c2fc2a5b65fc9aca20b4c85ef644f30ae88892ca0c0aec1143c0ea3"},"schema_version":"1.0"},"canonical_sha256":"c080ed1aef84502b3b0549cadb96f4c38eaf373932c96b42fe81acc3304954c1","source":{"kind":"arxiv","id":"2109.15301","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.15301","created_at":"2026-07-05T04:28:41Z"},{"alias_kind":"arxiv_version","alias_value":"2109.15301v3","created_at":"2026-07-05T04:28:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.15301","created_at":"2026-07-05T04:28:41Z"},{"alias_kind":"pith_short_12","alias_value":"YCAO2GXPQRIC","created_at":"2026-07-05T04:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"YCAO2GXPQRICWOYF","created_at":"2026-07-05T04:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"YCAO2GXP","created_at":"2026-07-05T04:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:YCAO2GXPQRICWOYFJHFNXFXUYO","target":"record","payload":{"canonical_record":{"source":{"id":"2109.15301","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2021-09-30T17:47:22Z","cross_cats_sorted":["hep-ph","nucl-ex"],"title_canon_sha256":"4f78374c2be52a52296108858412756490f1bfd02e16a4d4cea406f2abd4161e","abstract_canon_sha256":"b910e8fd4c2fc2a5b65fc9aca20b4c85ef644f30ae88892ca0c0aec1143c0ea3"},"schema_version":"1.0"},"canonical_sha256":"c080ed1aef84502b3b0549cadb96f4c38eaf373932c96b42fe81acc3304954c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:28:41.212176Z","signature_b64":"cT37/731D/TK6FL4valModoVD3cMGO3NYXlflhyRYyRRJQi0XLcCY5pXNVHwCr7TfREylSc6ieonxCks9YKTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c080ed1aef84502b3b0549cadb96f4c38eaf373932c96b42fe81acc3304954c1","last_reissued_at":"2026-07-05T04:28:41.211695Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:28:41.211695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.15301","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:28:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+hBIfDRDLG9BxISihnoUsk+QlSgZVTLvtbZLLvH8vCytbsurmSoBvLB9WxBpAev2ykSG8mD0eaLMjtm3tBKBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:18:05.801618Z"},"content_sha256":"a5c7c6c3eed72566036a4a18eed55bb8ab5580fcc59feebf478df7fd1540cb2b","schema_version":"1.0","event_id":"sha256:a5c7c6c3eed72566036a4a18eed55bb8ab5580fcc59feebf478df7fd1540cb2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:YCAO2GXPQRICWOYFJHFNXFXUYO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spin Polarization Formula for Dirac Fermions at Local Equilibrium","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","nucl-ex"],"primary_cat":"nucl-th","authors_text":"Xu-Guang Huang, Yu-Chen Liu","submitted_at":"2021-09-30T17:47:22Z","abstract_excerpt":"We derive a Cooper-Frye type spin polarization formula for Dirac fermions at local thermal equilibrium described by a grand canonical ensemble specified by temperature, fluid velocity, chemical potential, and spin potential. We discuss the physical meaning of different contributions to spin polarization and compare them with previous works. The present formula provides machinery to convert the spin potential computed in, e.g., relativistic spin hydrodynamics to the spin polarization observable in, e.g., heavy-ion collisions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.15301","kind":"arxiv","version":3},"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/2109.15301/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":"2026-07-05T04:28:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mHr3qYGRW0JuTo7PSZSihleewubBBXSxz+yWsIxEQnyb8BSnTbIci4yXHAXNntd0VuOz0l3yNI7vNu+AX2xaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:18:05.802186Z"},"content_sha256":"f7f9de8fd2ff7cc26ea1a9e9638250d870caf5f2ce4cf7217e83c02af8711700","schema_version":"1.0","event_id":"sha256:f7f9de8fd2ff7cc26ea1a9e9638250d870caf5f2ce4cf7217e83c02af8711700"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCAO2GXPQRICWOYFJHFNXFXUYO/bundle.json","state_url":"https://pith.science/pith/YCAO2GXPQRICWOYFJHFNXFXUYO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCAO2GXPQRICWOYFJHFNXFXUYO/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":"2026-08-16T22:18:05Z","links":{"resolver":"https://pith.science/pith/YCAO2GXPQRICWOYFJHFNXFXUYO","bundle":"https://pith.science/pith/YCAO2GXPQRICWOYFJHFNXFXUYO/bundle.json","state":"https://pith.science/pith/YCAO2GXPQRICWOYFJHFNXFXUYO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCAO2GXPQRICWOYFJHFNXFXUYO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YCAO2GXPQRICWOYFJHFNXFXUYO","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":"b910e8fd4c2fc2a5b65fc9aca20b4c85ef644f30ae88892ca0c0aec1143c0ea3","cross_cats_sorted":["hep-ph","nucl-ex"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2021-09-30T17:47:22Z","title_canon_sha256":"4f78374c2be52a52296108858412756490f1bfd02e16a4d4cea406f2abd4161e"},"schema_version":"1.0","source":{"id":"2109.15301","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.15301","created_at":"2026-07-05T04:28:41Z"},{"alias_kind":"arxiv_version","alias_value":"2109.15301v3","created_at":"2026-07-05T04:28:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.15301","created_at":"2026-07-05T04:28:41Z"},{"alias_kind":"pith_short_12","alias_value":"YCAO2GXPQRIC","created_at":"2026-07-05T04:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"YCAO2GXPQRICWOYF","created_at":"2026-07-05T04:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"YCAO2GXP","created_at":"2026-07-05T04:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:f7f9de8fd2ff7cc26ea1a9e9638250d870caf5f2ce4cf7217e83c02af8711700","target":"graph","created_at":"2026-07-05T04:28:41Z","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/2109.15301/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive a Cooper-Frye type spin polarization formula for Dirac fermions at local thermal equilibrium described by a grand canonical ensemble specified by temperature, fluid velocity, chemical potential, and spin potential. We discuss the physical meaning of different contributions to spin polarization and compare them with previous works. The present formula provides machinery to convert the spin potential computed in, e.g., relativistic spin hydrodynamics to the spin polarization observable in, e.g., heavy-ion collisions.","authors_text":"Xu-Guang Huang, Yu-Chen Liu","cross_cats":["hep-ph","nucl-ex"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2021-09-30T17:47:22Z","title":"Spin Polarization Formula for Dirac Fermions at Local Equilibrium"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.15301","kind":"arxiv","version":3},"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:a5c7c6c3eed72566036a4a18eed55bb8ab5580fcc59feebf478df7fd1540cb2b","target":"record","created_at":"2026-07-05T04:28:41Z","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":"b910e8fd4c2fc2a5b65fc9aca20b4c85ef644f30ae88892ca0c0aec1143c0ea3","cross_cats_sorted":["hep-ph","nucl-ex"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2021-09-30T17:47:22Z","title_canon_sha256":"4f78374c2be52a52296108858412756490f1bfd02e16a4d4cea406f2abd4161e"},"schema_version":"1.0","source":{"id":"2109.15301","kind":"arxiv","version":3}},"canonical_sha256":"c080ed1aef84502b3b0549cadb96f4c38eaf373932c96b42fe81acc3304954c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c080ed1aef84502b3b0549cadb96f4c38eaf373932c96b42fe81acc3304954c1","first_computed_at":"2026-07-05T04:28:41.211695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:28:41.211695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cT37/731D/TK6FL4valModoVD3cMGO3NYXlflhyRYyRRJQi0XLcCY5pXNVHwCr7TfREylSc6ieonxCks9YKTBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:28:41.212176Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.15301","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5c7c6c3eed72566036a4a18eed55bb8ab5580fcc59feebf478df7fd1540cb2b","sha256:f7f9de8fd2ff7cc26ea1a9e9638250d870caf5f2ce4cf7217e83c02af8711700"],"state_sha256":"9ed81eb3908567269241456d09ef6f0861f63d81f0311e35d854a6b26e480360"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dtLAISiWkL789wbvc8bcT8LfDj2mx6x8ysdTsXNBRLUXS/yDfXXs0xgBHsQpf6nWH+bkduxsFjkNkiEDmz5eBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T22:18:05.807100Z","bundle_sha256":"c1cb32e7ac960e8865c34e5f14d4e6426481856a8eee72c83c8f56a2b3265ed4"}}