{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:O2MNXYEQJGW6F6VSIYFH6WBOMQ","short_pith_number":"pith:O2MNXYEQ","canonical_record":{"source":{"id":"2209.12402","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2022-09-26T03:56:08Z","cross_cats_sorted":[],"title_canon_sha256":"57bb7148946e5dd36a3661cfcc3c8ff43d2b1f5aeffb53d73ff2401b08fbd61f","abstract_canon_sha256":"7f132834f0f1095a34ca3d3ddfaacebe2f3b9ff64076ff9f70e2dcb2809d86e2"},"schema_version":"1.0"},"canonical_sha256":"7698dbe09049ade2fab2460a7f582e641d52770061b96d61ffa07b9cabd61044","source":{"kind":"arxiv","id":"2209.12402","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.12402","created_at":"2026-07-05T05:22:55Z"},{"alias_kind":"arxiv_version","alias_value":"2209.12402v1","created_at":"2026-07-05T05:22:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.12402","created_at":"2026-07-05T05:22:55Z"},{"alias_kind":"pith_short_12","alias_value":"O2MNXYEQJGW6","created_at":"2026-07-05T05:22:55Z"},{"alias_kind":"pith_short_16","alias_value":"O2MNXYEQJGW6F6VS","created_at":"2026-07-05T05:22:55Z"},{"alias_kind":"pith_short_8","alias_value":"O2MNXYEQ","created_at":"2026-07-05T05:22:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:O2MNXYEQJGW6F6VSIYFH6WBOMQ","target":"record","payload":{"canonical_record":{"source":{"id":"2209.12402","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2022-09-26T03:56:08Z","cross_cats_sorted":[],"title_canon_sha256":"57bb7148946e5dd36a3661cfcc3c8ff43d2b1f5aeffb53d73ff2401b08fbd61f","abstract_canon_sha256":"7f132834f0f1095a34ca3d3ddfaacebe2f3b9ff64076ff9f70e2dcb2809d86e2"},"schema_version":"1.0"},"canonical_sha256":"7698dbe09049ade2fab2460a7f582e641d52770061b96d61ffa07b9cabd61044","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:22:55.333587Z","signature_b64":"Gj8OK7Pc9bOtzijZ31OjIk8SbN9GWSX093xP72wGNv3IPKRaQ0/wjP26SKbAAoqi8ilK9OQceJZGAXC+Ck8ADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7698dbe09049ade2fab2460a7f582e641d52770061b96d61ffa07b9cabd61044","last_reissued_at":"2026-07-05T05:22:55.333102Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:22:55.333102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.12402","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":"2026-07-05T05:22:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OGlvWaUoW4hHlDLPUZ7ShCSGO54UWdEr0n109Xb1vdCPvVXxQKs/vuDWBtK9RaJoXYwZJER51irXCFzio3fwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T13:39:58.553624Z"},"content_sha256":"9be19ef153f289b3a58f8204400ad6d7557ee2f8f77c6ab2ad7a1ee9aab4a6c1","schema_version":"1.0","event_id":"sha256:9be19ef153f289b3a58f8204400ad6d7557ee2f8f77c6ab2ad7a1ee9aab4a6c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:O2MNXYEQJGW6F6VSIYFH6WBOMQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spin Boltzmann equation for non-relativistic spin-1/2 fermions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"Qun Wang, Wen-Bo Dong, Yi-Liang Yin","submitted_at":"2022-09-26T03:56:08Z","abstract_excerpt":"We derive the spin Boltzmann equations for spin-1/2 fermions in a non-relativistic model with four-fermion contact interaction which conserves spin degrees of freedom. A great advantage of the model is that the spin matrix elements in collision terms can be completely worked out and be put into such a compact form that one can clearly see how spins are coupled in particle scatterings. A semi-classical expansion in the Planck constant has been made and the on-shell part of the spin Boltzmann equation up to the next-to-leading order is derived. At the leading order the equilibrium spin distribut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.12402","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.12402/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":"2026-07-05T05:22:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y5WcTjGLbYBU9v3k4+U/p2QMXhceWAJNpHwJSLUfJ938fhUr3AM8jvcMmyA+6zBpjkomkunknmspLEFe7z3gCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T13:39:58.554123Z"},"content_sha256":"bbd3bba261cdfb0af3dd6c70ac5e6a5396648d3da659e22dc1e94b13bc90ea40","schema_version":"1.0","event_id":"sha256:bbd3bba261cdfb0af3dd6c70ac5e6a5396648d3da659e22dc1e94b13bc90ea40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O2MNXYEQJGW6F6VSIYFH6WBOMQ/bundle.json","state_url":"https://pith.science/pith/O2MNXYEQJGW6F6VSIYFH6WBOMQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O2MNXYEQJGW6F6VSIYFH6WBOMQ/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":"2026-08-05T13:39:58Z","links":{"resolver":"https://pith.science/pith/O2MNXYEQJGW6F6VSIYFH6WBOMQ","bundle":"https://pith.science/pith/O2MNXYEQJGW6F6VSIYFH6WBOMQ/bundle.json","state":"https://pith.science/pith/O2MNXYEQJGW6F6VSIYFH6WBOMQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O2MNXYEQJGW6F6VSIYFH6WBOMQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:O2MNXYEQJGW6F6VSIYFH6WBOMQ","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":"7f132834f0f1095a34ca3d3ddfaacebe2f3b9ff64076ff9f70e2dcb2809d86e2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2022-09-26T03:56:08Z","title_canon_sha256":"57bb7148946e5dd36a3661cfcc3c8ff43d2b1f5aeffb53d73ff2401b08fbd61f"},"schema_version":"1.0","source":{"id":"2209.12402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.12402","created_at":"2026-07-05T05:22:55Z"},{"alias_kind":"arxiv_version","alias_value":"2209.12402v1","created_at":"2026-07-05T05:22:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.12402","created_at":"2026-07-05T05:22:55Z"},{"alias_kind":"pith_short_12","alias_value":"O2MNXYEQJGW6","created_at":"2026-07-05T05:22:55Z"},{"alias_kind":"pith_short_16","alias_value":"O2MNXYEQJGW6F6VS","created_at":"2026-07-05T05:22:55Z"},{"alias_kind":"pith_short_8","alias_value":"O2MNXYEQ","created_at":"2026-07-05T05:22:55Z"}],"graph_snapshots":[{"event_id":"sha256:bbd3bba261cdfb0af3dd6c70ac5e6a5396648d3da659e22dc1e94b13bc90ea40","target":"graph","created_at":"2026-07-05T05:22:55Z","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/2209.12402/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive the spin Boltzmann equations for spin-1/2 fermions in a non-relativistic model with four-fermion contact interaction which conserves spin degrees of freedom. A great advantage of the model is that the spin matrix elements in collision terms can be completely worked out and be put into such a compact form that one can clearly see how spins are coupled in particle scatterings. A semi-classical expansion in the Planck constant has been made and the on-shell part of the spin Boltzmann equation up to the next-to-leading order is derived. At the leading order the equilibrium spin distribut","authors_text":"Qun Wang, Wen-Bo Dong, Yi-Liang Yin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2022-09-26T03:56:08Z","title":"Spin Boltzmann equation for non-relativistic spin-1/2 fermions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.12402","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":"sha256:9be19ef153f289b3a58f8204400ad6d7557ee2f8f77c6ab2ad7a1ee9aab4a6c1","target":"record","created_at":"2026-07-05T05:22:55Z","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":"7f132834f0f1095a34ca3d3ddfaacebe2f3b9ff64076ff9f70e2dcb2809d86e2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nucl-th","submitted_at":"2022-09-26T03:56:08Z","title_canon_sha256":"57bb7148946e5dd36a3661cfcc3c8ff43d2b1f5aeffb53d73ff2401b08fbd61f"},"schema_version":"1.0","source":{"id":"2209.12402","kind":"arxiv","version":1}},"canonical_sha256":"7698dbe09049ade2fab2460a7f582e641d52770061b96d61ffa07b9cabd61044","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7698dbe09049ade2fab2460a7f582e641d52770061b96d61ffa07b9cabd61044","first_computed_at":"2026-07-05T05:22:55.333102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:22:55.333102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gj8OK7Pc9bOtzijZ31OjIk8SbN9GWSX093xP72wGNv3IPKRaQ0/wjP26SKbAAoqi8ilK9OQceJZGAXC+Ck8ADQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:22:55.333587Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.12402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9be19ef153f289b3a58f8204400ad6d7557ee2f8f77c6ab2ad7a1ee9aab4a6c1","sha256:bbd3bba261cdfb0af3dd6c70ac5e6a5396648d3da659e22dc1e94b13bc90ea40"],"state_sha256":"deefae8c097da9eec935e4e9977cc3e7bc256579f52d8468bfaf531ba17cb8f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0XHRnF859/CTmtxFZBugEccN2SOUKR3zL4MiJ/FvThtv1yEcELZr7Y3yz9x/gwo2nmt2y8pF13N/R9Q/IG1VCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T13:39:58.558141Z","bundle_sha256":"b27f8338e5ecdcd5908d3cd7fba7d8dc7bca8416933fdc4574f0d8d68585de47"}}