{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:X6ISXQEVANAKA7BAGPVHJVLBPG","short_pith_number":"pith:X6ISXQEV","canonical_record":{"source":{"id":"astro-ph/0002502","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2000-02-28T08:21:52Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"f26eca65ab4fa97ddc5c8cef2207b39adb00efd19e43f2d57e551acfecd59a1f","abstract_canon_sha256":"c32d5f23db6abb6417fb7d81b1ed2829595c60b4072fd40be689c5f55390ac11"},"schema_version":"1.0"},"canonical_sha256":"bf912bc0950340a07c2033ea74d561799ca0b511e2bd03b080cd9bdc345b2111","source":{"kind":"arxiv","id":"astro-ph/0002502","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0002502","created_at":"2026-07-04T16:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0002502v1","created_at":"2026-07-04T16:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0002502","created_at":"2026-07-04T16:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"X6ISXQEVANAK","created_at":"2026-07-04T16:16:07Z"},{"alias_kind":"pith_short_16","alias_value":"X6ISXQEVANAKA7BA","created_at":"2026-07-04T16:16:07Z"},{"alias_kind":"pith_short_8","alias_value":"X6ISXQEV","created_at":"2026-07-04T16:16:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:X6ISXQEVANAKA7BAGPVHJVLBPG","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/0002502","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2000-02-28T08:21:52Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"f26eca65ab4fa97ddc5c8cef2207b39adb00efd19e43f2d57e551acfecd59a1f","abstract_canon_sha256":"c32d5f23db6abb6417fb7d81b1ed2829595c60b4072fd40be689c5f55390ac11"},"schema_version":"1.0"},"canonical_sha256":"bf912bc0950340a07c2033ea74d561799ca0b511e2bd03b080cd9bdc345b2111","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:16:07.360733Z","signature_b64":"CVVbqco69dzNUXPLbCRxyyL2iisFbnrA9DWicnrFI4z3vPnvsuC1QyHNWzvr7TpQ7VqwuZcZP2T8wBEPWldZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf912bc0950340a07c2033ea74d561799ca0b511e2bd03b080cd9bdc345b2111","last_reissued_at":"2026-07-04T16:16:07.360255Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:16:07.360255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/0002502","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":"2026-07-04T16:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BM/QHgKP3odPUaqHglnQH+NT8GE5RekP9cpaD2o7Z/78ntzFicUXjfTMoDHnO34xiltOf2r3C6yKYyO3uF5+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:14:52.452012Z"},"content_sha256":"bebcb696d89ae324b377fea44cdc84baf9c7893067e5dafff102850618df4e06","schema_version":"1.0","event_id":"sha256:bebcb696d89ae324b377fea44cdc84baf9c7893067e5dafff102850618df4e06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:X6ISXQEVANAKA7BAGPVHJVLBPG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boltzmann equations for neutrinos with flavor mixings","license":"","headline":"","cross_cats":["hep-ph"],"primary_cat":"astro-ph","authors_text":"Shoichi Yamada (RESCEU, University of Tokyo)","submitted_at":"2000-02-28T08:21:52Z","abstract_excerpt":"With a view of applications to the simulations of supernova explosion and proto neutron star cooling, we derive the Boltzmann equations for the neutrino transport with the flavor mixing based on the real time formalism of the nonequilibrium field theory and the gradient expansion of the Green function. The relativistic kinematics is properly taken into account. The advection terms are derived in the mean field approximation for the neutrino self-energy whiles the collision terms are obtained in the Born approximation. The resulting equations take the familiar form of the Boltzmann equation wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0002502","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/astro-ph/0002502/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":"2026-07-04T16:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2TGKsZcZMCgYRUzi9r3dgwImk3UbDmLRQewYB+Ea4iBAXKy5cq0E1vxTve0ajV0ONhtW3Im9KWEHNMq+zVxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T19:14:52.452546Z"},"content_sha256":"7588579b60ef7ba1d245492d63399b0f3b98747e0b328cbd1e1597a28e49a05d","schema_version":"1.0","event_id":"sha256:7588579b60ef7ba1d245492d63399b0f3b98747e0b328cbd1e1597a28e49a05d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X6ISXQEVANAKA7BAGPVHJVLBPG/bundle.json","state_url":"https://pith.science/pith/X6ISXQEVANAKA7BAGPVHJVLBPG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X6ISXQEVANAKA7BAGPVHJVLBPG/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":"2026-08-09T19:14:52Z","links":{"resolver":"https://pith.science/pith/X6ISXQEVANAKA7BAGPVHJVLBPG","bundle":"https://pith.science/pith/X6ISXQEVANAKA7BAGPVHJVLBPG/bundle.json","state":"https://pith.science/pith/X6ISXQEVANAKA7BAGPVHJVLBPG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X6ISXQEVANAKA7BAGPVHJVLBPG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:X6ISXQEVANAKA7BAGPVHJVLBPG","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":"c32d5f23db6abb6417fb7d81b1ed2829595c60b4072fd40be689c5f55390ac11","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"astro-ph","submitted_at":"2000-02-28T08:21:52Z","title_canon_sha256":"f26eca65ab4fa97ddc5c8cef2207b39adb00efd19e43f2d57e551acfecd59a1f"},"schema_version":"1.0","source":{"id":"astro-ph/0002502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0002502","created_at":"2026-07-04T16:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0002502v1","created_at":"2026-07-04T16:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0002502","created_at":"2026-07-04T16:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"X6ISXQEVANAK","created_at":"2026-07-04T16:16:07Z"},{"alias_kind":"pith_short_16","alias_value":"X6ISXQEVANAKA7BA","created_at":"2026-07-04T16:16:07Z"},{"alias_kind":"pith_short_8","alias_value":"X6ISXQEV","created_at":"2026-07-04T16:16:07Z"}],"graph_snapshots":[{"event_id":"sha256:7588579b60ef7ba1d245492d63399b0f3b98747e0b328cbd1e1597a28e49a05d","target":"graph","created_at":"2026-07-04T16:16:07Z","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/astro-ph/0002502/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"With a view of applications to the simulations of supernova explosion and proto neutron star cooling, we derive the Boltzmann equations for the neutrino transport with the flavor mixing based on the real time formalism of the nonequilibrium field theory and the gradient expansion of the Green function. The relativistic kinematics is properly taken into account. The advection terms are derived in the mean field approximation for the neutrino self-energy whiles the collision terms are obtained in the Born approximation. The resulting equations take the familiar form of the Boltzmann equation wit","authors_text":"Shoichi Yamada (RESCEU, University of Tokyo)","cross_cats":["hep-ph"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2000-02-28T08:21:52Z","title":"Boltzmann equations for neutrinos with flavor mixings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0002502","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:bebcb696d89ae324b377fea44cdc84baf9c7893067e5dafff102850618df4e06","target":"record","created_at":"2026-07-04T16:16:07Z","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":"c32d5f23db6abb6417fb7d81b1ed2829595c60b4072fd40be689c5f55390ac11","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"astro-ph","submitted_at":"2000-02-28T08:21:52Z","title_canon_sha256":"f26eca65ab4fa97ddc5c8cef2207b39adb00efd19e43f2d57e551acfecd59a1f"},"schema_version":"1.0","source":{"id":"astro-ph/0002502","kind":"arxiv","version":1}},"canonical_sha256":"bf912bc0950340a07c2033ea74d561799ca0b511e2bd03b080cd9bdc345b2111","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf912bc0950340a07c2033ea74d561799ca0b511e2bd03b080cd9bdc345b2111","first_computed_at":"2026-07-04T16:16:07.360255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:16:07.360255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CVVbqco69dzNUXPLbCRxyyL2iisFbnrA9DWicnrFI4z3vPnvsuC1QyHNWzvr7TpQ7VqwuZcZP2T8wBEPWldZAA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:16:07.360733Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0002502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bebcb696d89ae324b377fea44cdc84baf9c7893067e5dafff102850618df4e06","sha256:7588579b60ef7ba1d245492d63399b0f3b98747e0b328cbd1e1597a28e49a05d"],"state_sha256":"296c9511d095a6eb608fed4cbb342f2aac4e4257c06c1c69c4844d3e0a4533bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VixOdKMZSS7MBuBTXRfI6cu+Xt6U5I262Jxvvh9h7+PsVZQRmT9iMzz1eGsBM7A9eyhcydxKC16aVKXLGx67Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T19:14:52.456753Z","bundle_sha256":"9b00c16937513985218a4e375e4ca98adf52667ec06f1f69567a7eb88506537a"}}