{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:5RFNXGFXMIG6LRNYP2DTR6PFGG","short_pith_number":"pith:5RFNXGFX","schema_version":"1.0","canonical_sha256":"ec4adb98b7620de5c5b87e8738f9e5318228f2959c305f8171b2e3a6a791396f","source":{"kind":"arxiv","id":"1002.0426","version":1},"attestation_state":"computed","paper":{"title":"Spin kinetic theory - quantum kinetic theory in extended phase space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"G. Brodin, J. Zamanian, M. Marklund","submitted_at":"2010-02-02T09:03:52Z","abstract_excerpt":"The concept of phase space distribution functions and their evolution is used in the case of en enlarged phase space. In particular, we include the intrinsic spin of particles and present a quantum kinetic evolution equation for a scalar quasi-distribution function. In contrast to the proper Wigner transformation technique, for which we expect the corresponding quasi-distribution function to be a complex matrix, we introduce a spin projection operator for the density matrix in order to obtain the aforementioned scalar quasi-distribution function. There is a close correspondence between this pr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1002.0426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-02-02T09:03:52Z","cross_cats_sorted":[],"title_canon_sha256":"e3e0c5dea19bbd1023ef19f34af6a96e35968292c90d11605804c4fb8453c0ce","abstract_canon_sha256":"d0ff7654d9865f42a6656e87fa6e3236d2b18a28bb39bd02d4938488fc34bc61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:21.084220Z","signature_b64":"wZ/uSqZmefDv7k5M5R2uhSNyDQYeBlxsYEFM4uwNFQnyKnlFlHi5TERhl16s2SAaYnZC/BfSJOsASV91StdFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec4adb98b7620de5c5b87e8738f9e5318228f2959c305f8171b2e3a6a791396f","last_reissued_at":"2026-05-18T02:09:21.083532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:21.083532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spin kinetic theory - quantum kinetic theory in extended phase space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"G. Brodin, J. Zamanian, M. Marklund","submitted_at":"2010-02-02T09:03:52Z","abstract_excerpt":"The concept of phase space distribution functions and their evolution is used in the case of en enlarged phase space. In particular, we include the intrinsic spin of particles and present a quantum kinetic evolution equation for a scalar quasi-distribution function. In contrast to the proper Wigner transformation technique, for which we expect the corresponding quasi-distribution function to be a complex matrix, we introduce a spin projection operator for the density matrix in order to obtain the aforementioned scalar quasi-distribution function. There is a close correspondence between this pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0426","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1002.0426","created_at":"2026-05-18T02:09:21.083641+00:00"},{"alias_kind":"arxiv_version","alias_value":"1002.0426v1","created_at":"2026-05-18T02:09:21.083641+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0426","created_at":"2026-05-18T02:09:21.083641+00:00"},{"alias_kind":"pith_short_12","alias_value":"5RFNXGFXMIG6","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"5RFNXGFXMIG6LRNY","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"5RFNXGFX","created_at":"2026-05-18T12:26:04.259169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5RFNXGFXMIG6LRNYP2DTR6PFGG","json":"https://pith.science/pith/5RFNXGFXMIG6LRNYP2DTR6PFGG.json","graph_json":"https://pith.science/api/pith-number/5RFNXGFXMIG6LRNYP2DTR6PFGG/graph.json","events_json":"https://pith.science/api/pith-number/5RFNXGFXMIG6LRNYP2DTR6PFGG/events.json","paper":"https://pith.science/paper/5RFNXGFX"},"agent_actions":{"view_html":"https://pith.science/pith/5RFNXGFXMIG6LRNYP2DTR6PFGG","download_json":"https://pith.science/pith/5RFNXGFXMIG6LRNYP2DTR6PFGG.json","view_paper":"https://pith.science/paper/5RFNXGFX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1002.0426&json=true","fetch_graph":"https://pith.science/api/pith-number/5RFNXGFXMIG6LRNYP2DTR6PFGG/graph.json","fetch_events":"https://pith.science/api/pith-number/5RFNXGFXMIG6LRNYP2DTR6PFGG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5RFNXGFXMIG6LRNYP2DTR6PFGG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5RFNXGFXMIG6LRNYP2DTR6PFGG/action/storage_attestation","attest_author":"https://pith.science/pith/5RFNXGFXMIG6LRNYP2DTR6PFGG/action/author_attestation","sign_citation":"https://pith.science/pith/5RFNXGFXMIG6LRNYP2DTR6PFGG/action/citation_signature","submit_replication":"https://pith.science/pith/5RFNXGFXMIG6LRNYP2DTR6PFGG/action/replication_record"}},"created_at":"2026-05-18T02:09:21.083641+00:00","updated_at":"2026-05-18T02:09:21.083641+00:00"}