{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:MPZLCLOVQEDTH7E6VZH2FCYVC6","short_pith_number":"pith:MPZLCLOV","canonical_record":{"source":{"id":"astro-ph/0703776","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2007-03-29T21:40:10Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"7a2a6cf291a782956e58e65a084052cc48db75a8c27fc420e232468ec3ffd2c7","abstract_canon_sha256":"c8aed8689ad8b31fe6abf70a522a5bbfd58106ce27d668c2c94992324921b062"},"schema_version":"1.0"},"canonical_sha256":"63f2b12dd5810733fc9eae4fa28b15179d422be427deded89d9dad20109f6c02","source":{"kind":"arxiv","id":"astro-ph/0703776","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0703776","created_at":"2026-07-04T15:21:58Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0703776v1","created_at":"2026-07-04T15:21:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0703776","created_at":"2026-07-04T15:21:58Z"},{"alias_kind":"pith_short_12","alias_value":"MPZLCLOVQEDT","created_at":"2026-07-04T15:21:58Z"},{"alias_kind":"pith_short_16","alias_value":"MPZLCLOVQEDTH7E6","created_at":"2026-07-04T15:21:58Z"},{"alias_kind":"pith_short_8","alias_value":"MPZLCLOV","created_at":"2026-07-04T15:21:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:MPZLCLOVQEDTH7E6VZH2FCYVC6","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/0703776","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2007-03-29T21:40:10Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"7a2a6cf291a782956e58e65a084052cc48db75a8c27fc420e232468ec3ffd2c7","abstract_canon_sha256":"c8aed8689ad8b31fe6abf70a522a5bbfd58106ce27d668c2c94992324921b062"},"schema_version":"1.0"},"canonical_sha256":"63f2b12dd5810733fc9eae4fa28b15179d422be427deded89d9dad20109f6c02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:21:58.339469Z","signature_b64":"+05CqJkZjYYR2fTOjq5my2gNIv+UTkxOIbVqVJFiCf8baMwuUayiYFhEhxsrtKmxo4x0OTNIJIKB/7m9oKrECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63f2b12dd5810733fc9eae4fa28b15179d422be427deded89d9dad20109f6c02","last_reissued_at":"2026-07-04T15:21:58.338991Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:21:58.338991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/0703776","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":"2026-07-04T15:21:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9EQyalyS+a2pMV4PwQMViGzmmfCuju/qVLYJn60Sny5bPO/h6xPtB0sUOtm3FZzueR7JSgxT2oLDna0KkcR3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:09:58.927774Z"},"content_sha256":"c084cbf0a999e55e8d2e09ec95b361d4ef9a8dd441f320dcbd24f4de2ecc7967","schema_version":"1.0","event_id":"sha256:c084cbf0a999e55e8d2e09ec95b361d4ef9a8dd441f320dcbd24f4de2ecc7967"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:MPZLCLOVQEDTH7E6VZH2FCYVC6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of Collective Neutrino Flavor Transformation in Supernovae","license":"","headline":"","cross_cats":["hep-ph"],"primary_cat":"astro-ph","authors_text":"George M. Fuller (UCSD), Huaiyu Duan (UCSD), J. Carlson (LANL), Yong-Zhong Qian (UMN)","submitted_at":"2007-03-29T21:40:10Z","abstract_excerpt":"We study the flavor evolution of a dense gas initially consisting of pure mono-energetic $\\nu_e$ and $\\bar\\nu_e$. Using adiabatic invariants and the special symmetry in such a system we are able to calculate the flavor evolution of the neutrino gas for the cases with slowly decreasing neutrino number densities. These calculations give new insights into the results of recent large-scale numerical simulations of neutrino flavor transformation in supernovae. For example, our calculations reveal the existence of what we term the ``collective precession mode''. Our analyses suggest that neutrinos w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0703776","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/0703776/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":"2026-07-04T15:21:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WnrKwya2TQa+E7DKksDz2mPAwV/O32jBjfNVO8MMFYdra1XL2L6MdSgTGTc58zovj7Oea4RVPA55LbT53C0eDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T20:09:58.928315Z"},"content_sha256":"7a2ff97b3ab5b4251b2093e2228340e12a45d3995bdca6ef3c8ecded3d1e2bf4","schema_version":"1.0","event_id":"sha256:7a2ff97b3ab5b4251b2093e2228340e12a45d3995bdca6ef3c8ecded3d1e2bf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MPZLCLOVQEDTH7E6VZH2FCYVC6/bundle.json","state_url":"https://pith.science/pith/MPZLCLOVQEDTH7E6VZH2FCYVC6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MPZLCLOVQEDTH7E6VZH2FCYVC6/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":"2026-08-09T20:09:58Z","links":{"resolver":"https://pith.science/pith/MPZLCLOVQEDTH7E6VZH2FCYVC6","bundle":"https://pith.science/pith/MPZLCLOVQEDTH7E6VZH2FCYVC6/bundle.json","state":"https://pith.science/pith/MPZLCLOVQEDTH7E6VZH2FCYVC6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MPZLCLOVQEDTH7E6VZH2FCYVC6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:MPZLCLOVQEDTH7E6VZH2FCYVC6","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":"c8aed8689ad8b31fe6abf70a522a5bbfd58106ce27d668c2c94992324921b062","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"astro-ph","submitted_at":"2007-03-29T21:40:10Z","title_canon_sha256":"7a2a6cf291a782956e58e65a084052cc48db75a8c27fc420e232468ec3ffd2c7"},"schema_version":"1.0","source":{"id":"astro-ph/0703776","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0703776","created_at":"2026-07-04T15:21:58Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0703776v1","created_at":"2026-07-04T15:21:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0703776","created_at":"2026-07-04T15:21:58Z"},{"alias_kind":"pith_short_12","alias_value":"MPZLCLOVQEDT","created_at":"2026-07-04T15:21:58Z"},{"alias_kind":"pith_short_16","alias_value":"MPZLCLOVQEDTH7E6","created_at":"2026-07-04T15:21:58Z"},{"alias_kind":"pith_short_8","alias_value":"MPZLCLOV","created_at":"2026-07-04T15:21:58Z"}],"graph_snapshots":[{"event_id":"sha256:7a2ff97b3ab5b4251b2093e2228340e12a45d3995bdca6ef3c8ecded3d1e2bf4","target":"graph","created_at":"2026-07-04T15:21:58Z","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/0703776/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the flavor evolution of a dense gas initially consisting of pure mono-energetic $\\nu_e$ and $\\bar\\nu_e$. Using adiabatic invariants and the special symmetry in such a system we are able to calculate the flavor evolution of the neutrino gas for the cases with slowly decreasing neutrino number densities. These calculations give new insights into the results of recent large-scale numerical simulations of neutrino flavor transformation in supernovae. For example, our calculations reveal the existence of what we term the ``collective precession mode''. Our analyses suggest that neutrinos w","authors_text":"George M. Fuller (UCSD), Huaiyu Duan (UCSD), J. Carlson (LANL), Yong-Zhong Qian (UMN)","cross_cats":["hep-ph"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2007-03-29T21:40:10Z","title":"Analysis of Collective Neutrino Flavor Transformation in Supernovae"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0703776","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:c084cbf0a999e55e8d2e09ec95b361d4ef9a8dd441f320dcbd24f4de2ecc7967","target":"record","created_at":"2026-07-04T15:21:58Z","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":"c8aed8689ad8b31fe6abf70a522a5bbfd58106ce27d668c2c94992324921b062","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"astro-ph","submitted_at":"2007-03-29T21:40:10Z","title_canon_sha256":"7a2a6cf291a782956e58e65a084052cc48db75a8c27fc420e232468ec3ffd2c7"},"schema_version":"1.0","source":{"id":"astro-ph/0703776","kind":"arxiv","version":1}},"canonical_sha256":"63f2b12dd5810733fc9eae4fa28b15179d422be427deded89d9dad20109f6c02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63f2b12dd5810733fc9eae4fa28b15179d422be427deded89d9dad20109f6c02","first_computed_at":"2026-07-04T15:21:58.338991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:21:58.338991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+05CqJkZjYYR2fTOjq5my2gNIv+UTkxOIbVqVJFiCf8baMwuUayiYFhEhxsrtKmxo4x0OTNIJIKB/7m9oKrECg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:21:58.339469Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0703776","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c084cbf0a999e55e8d2e09ec95b361d4ef9a8dd441f320dcbd24f4de2ecc7967","sha256:7a2ff97b3ab5b4251b2093e2228340e12a45d3995bdca6ef3c8ecded3d1e2bf4"],"state_sha256":"3cd0e5c10bc019948963b2caa6af66ded0dcb951becf72f8501196d47d1183e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ZcNB7mIckkeNBbj40Drinssvxn1AxraTEBXfyZaxlId7/65QjLDdGxTWC2OlylWEaLLC/kjcBnP1IkXg8mFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T20:09:58.932607Z","bundle_sha256":"6e455bd8bd239669c3bcbbafcbe7faa64b101973cff73d71535532474892efaf"}}