{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:4REYDWOQTYH3NJCD7UT7RXVUOO","short_pith_number":"pith:4REYDWOQ","canonical_record":{"source":{"id":"astro-ph/0305390","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2003-05-21T07:31:55Z","cross_cats_sorted":[],"title_canon_sha256":"399f3aa813522111271d570c876b9550604cb566783cdc1e663a0b6e0ee60ead","abstract_canon_sha256":"1a47d6ed2c3987fa3091fbb157f5a505137ee685407aace16db94bf7dfce4386"},"schema_version":"1.0"},"canonical_sha256":"e44981d9d09e0fb6a443fd27f8deb4738f71b7de9716081a1c717bcd8a3f6bf9","source":{"kind":"arxiv","id":"astro-ph/0305390","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0305390","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0305390v1","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0305390","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"4REYDWOQTYH3","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"4REYDWOQTYH3NJCD","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"4REYDWOQ","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:4REYDWOQTYH3NJCD7UT7RXVUOO","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/0305390","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2003-05-21T07:31:55Z","cross_cats_sorted":[],"title_canon_sha256":"399f3aa813522111271d570c876b9550604cb566783cdc1e663a0b6e0ee60ead","abstract_canon_sha256":"1a47d6ed2c3987fa3091fbb157f5a505137ee685407aace16db94bf7dfce4386"},"schema_version":"1.0"},"canonical_sha256":"e44981d9d09e0fb6a443fd27f8deb4738f71b7de9716081a1c717bcd8a3f6bf9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:37.337961Z","signature_b64":"MDII1pi/T4Zb0sRkZV/z4Ewo2JNiHNUKdooqmRArHW9XMNjy3gnIZs/aJr90+66Ys9DaBX//eaNZfz8TIMO5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e44981d9d09e0fb6a443fd27f8deb4738f71b7de9716081a1c717bcd8a3f6bf9","last_reissued_at":"2026-05-18T04:13:37.337411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:37.337411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/0305390","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":"2026-05-18T04:13:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tv6ZWSehmlMzqPaeUEP4g/Dapvj5BZZuYaR9rph/D9Lp+w/ANwczLrJq7MoCxy9fQUdhp8nHaHgBEjBBIYD4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:41:38.971828Z"},"content_sha256":"88eacb4ffd90c5a891be43dbc7ffdf63b848612f074a03b1042cad6a2ce4dec0","schema_version":"1.0","event_id":"sha256:88eacb4ffd90c5a891be43dbc7ffdf63b848612f074a03b1042cad6a2ce4dec0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:4REYDWOQTYH3NJCD7UT7RXVUOO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Covariant Wigner Function Approach to the Boltzmann Equation for Mixing Fermions in Curved Spacetime","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Kazuhiro Yamamoto","submitted_at":"2003-05-21T07:31:55Z","abstract_excerpt":"Based on the covariant Wigner function approach we derive the quantum Boltzmann equation for fermions with flavor mixing in general curved spacetime. This work gives a rigorous theoretical framework to investigate the flavor oscillation phenomena taking the gravitational effect into account. It is shown that the Boltzmann equation of the lowest order of the expansion with respect to $\\hbar$ reproduces the previous result which was derived in the relativistic limit on the Minkowski background spacetime. It is demonstrated that the familiar formula for the vacuum neutrino oscillation can be obta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0305390","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:13:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0cSzW9JZpbYjVtxkXSsju/COHUACH/QwPGRrg7Zi64BrHlaBK99LAmpGbjcB5tMvfYP4nKEstYSYYZlP43bMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:41:38.972184Z"},"content_sha256":"db2fccdfeb850209abe86eb3e71fd2bb51a891c3dd42d0d8a9a843bfe76d21cb","schema_version":"1.0","event_id":"sha256:db2fccdfeb850209abe86eb3e71fd2bb51a891c3dd42d0d8a9a843bfe76d21cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4REYDWOQTYH3NJCD7UT7RXVUOO/bundle.json","state_url":"https://pith.science/pith/4REYDWOQTYH3NJCD7UT7RXVUOO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4REYDWOQTYH3NJCD7UT7RXVUOO/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":"2026-05-25T12:41:38Z","links":{"resolver":"https://pith.science/pith/4REYDWOQTYH3NJCD7UT7RXVUOO","bundle":"https://pith.science/pith/4REYDWOQTYH3NJCD7UT7RXVUOO/bundle.json","state":"https://pith.science/pith/4REYDWOQTYH3NJCD7UT7RXVUOO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4REYDWOQTYH3NJCD7UT7RXVUOO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:4REYDWOQTYH3NJCD7UT7RXVUOO","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":"1a47d6ed2c3987fa3091fbb157f5a505137ee685407aace16db94bf7dfce4386","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2003-05-21T07:31:55Z","title_canon_sha256":"399f3aa813522111271d570c876b9550604cb566783cdc1e663a0b6e0ee60ead"},"schema_version":"1.0","source":{"id":"astro-ph/0305390","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0305390","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0305390v1","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0305390","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"4REYDWOQTYH3","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"4REYDWOQTYH3NJCD","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"4REYDWOQ","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:db2fccdfeb850209abe86eb3e71fd2bb51a891c3dd42d0d8a9a843bfe76d21cb","target":"graph","created_at":"2026-05-18T04:13:37Z","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":"Based on the covariant Wigner function approach we derive the quantum Boltzmann equation for fermions with flavor mixing in general curved spacetime. This work gives a rigorous theoretical framework to investigate the flavor oscillation phenomena taking the gravitational effect into account. It is shown that the Boltzmann equation of the lowest order of the expansion with respect to $\\hbar$ reproduces the previous result which was derived in the relativistic limit on the Minkowski background spacetime. It is demonstrated that the familiar formula for the vacuum neutrino oscillation can be obta","authors_text":"Kazuhiro Yamamoto","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2003-05-21T07:31:55Z","title":"Covariant Wigner Function Approach to the Boltzmann Equation for Mixing Fermions in Curved Spacetime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0305390","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":"sha256:88eacb4ffd90c5a891be43dbc7ffdf63b848612f074a03b1042cad6a2ce4dec0","target":"record","created_at":"2026-05-18T04:13:37Z","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":"1a47d6ed2c3987fa3091fbb157f5a505137ee685407aace16db94bf7dfce4386","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2003-05-21T07:31:55Z","title_canon_sha256":"399f3aa813522111271d570c876b9550604cb566783cdc1e663a0b6e0ee60ead"},"schema_version":"1.0","source":{"id":"astro-ph/0305390","kind":"arxiv","version":1}},"canonical_sha256":"e44981d9d09e0fb6a443fd27f8deb4738f71b7de9716081a1c717bcd8a3f6bf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e44981d9d09e0fb6a443fd27f8deb4738f71b7de9716081a1c717bcd8a3f6bf9","first_computed_at":"2026-05-18T04:13:37.337411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:37.337411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MDII1pi/T4Zb0sRkZV/z4Ewo2JNiHNUKdooqmRArHW9XMNjy3gnIZs/aJr90+66Ys9DaBX//eaNZfz8TIMO5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:37.337961Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0305390","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88eacb4ffd90c5a891be43dbc7ffdf63b848612f074a03b1042cad6a2ce4dec0","sha256:db2fccdfeb850209abe86eb3e71fd2bb51a891c3dd42d0d8a9a843bfe76d21cb"],"state_sha256":"2ee293e0173720f471b855b7f288daaa9c5a84a12fec629b1e397047b1c2bf76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fBfNUh+mv8tBQtk1wp3soGwtrmTVUutI/BK3i/iV4WNmtITsdolzGSfaZ04PMRs3gXH5E0jO8lJBICv+WgAeAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:41:38.974429Z","bundle_sha256":"4d128db0c15c770d5ad8293f33c616438397f657e3749d1390ae7901cbcc2256"}}