{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:52RNVKU4BE6JMM5TFGTYT3CKO5","short_pith_number":"pith:52RNVKU4","canonical_record":{"source":{"id":"0801.1363","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2008-01-09T19:02:58Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"937a7aee08a44f5207c8c1289bf39c4ca181bbfebb2a6daf572f195409001490","abstract_canon_sha256":"cf1e35ef558038a99b9b31feba3e74becb8f74681832bad18a94c5e2b49821d6"},"schema_version":"1.0"},"canonical_sha256":"eea2daaa9c093c9633b329a789ec4a7748cfec8641183effd7bcf237235e4e3d","source":{"kind":"arxiv","id":"0801.1363","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1363","created_at":"2026-07-04T15:30:52Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1363v2","created_at":"2026-07-04T15:30:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1363","created_at":"2026-07-04T15:30:52Z"},{"alias_kind":"pith_short_12","alias_value":"52RNVKU4BE6J","created_at":"2026-07-04T15:30:52Z"},{"alias_kind":"pith_short_16","alias_value":"52RNVKU4BE6JMM5T","created_at":"2026-07-04T15:30:52Z"},{"alias_kind":"pith_short_8","alias_value":"52RNVKU4","created_at":"2026-07-04T15:30:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:52RNVKU4BE6JMM5TFGTYT3CKO5","target":"record","payload":{"canonical_record":{"source":{"id":"0801.1363","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2008-01-09T19:02:58Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"937a7aee08a44f5207c8c1289bf39c4ca181bbfebb2a6daf572f195409001490","abstract_canon_sha256":"cf1e35ef558038a99b9b31feba3e74becb8f74681832bad18a94c5e2b49821d6"},"schema_version":"1.0"},"canonical_sha256":"eea2daaa9c093c9633b329a789ec4a7748cfec8641183effd7bcf237235e4e3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:30:52.856629Z","signature_b64":"LmHL++ilXWV7KethMg+MzbAy8dyz0G4zmGC38tfX9ZrADxLJ5hLfke65GNtH1qDLI78aElVS5EdMiJ/+yPukCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eea2daaa9c093c9633b329a789ec4a7748cfec8641183effd7bcf237235e4e3d","last_reissued_at":"2026-07-04T15:30:52.856251Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:30:52.856251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.1363","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:30:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c5RxKgSus0dVX070rD4F8mhTxeQj9zuJe0M0Za2kmVstgjYydQuquYdd8mOB3ImFwXIqCtHocaGd9geLQuG4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T12:41:20.679953Z"},"content_sha256":"57c58dde84914d0531de37bbfe9a038d51f1c725c83030135e513759c9cf42d5","schema_version":"1.0","event_id":"sha256:57c58dde84914d0531de37bbfe9a038d51f1c725c83030135e513759c9cf42d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:52RNVKU4BE6JMM5TFGTYT3CKO5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stepwise Spectral Swapping with Three Neutrino Flavors","license":"","headline":"","cross_cats":["hep-ph"],"primary_cat":"astro-ph","authors_text":"George M. Fuller, Huaiyu Duan, Yong-Zhong Qian","submitted_at":"2008-01-09T19:02:58Z","abstract_excerpt":"We develop a framework for studying collective three-flavor neutrino oscillations based on the density matrix formalism. We show how techniques proven useful for collective two-flavor neutrino oscillations such as corotating frames can be applied readily to three-flavor mixing. Applying two simple assumptions and the conservation of two ``lepton numbers'' we use this framework to demonstrate how the adiabatic/precession solution emerges. We illustrate with a numerical example how two stepwise spectral swaps appear naturally if the flavor evolution of the neutrino gas can be described by such a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1363","kind":"arxiv","version":2},"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/0801.1363/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":"2026-07-04T15:30:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KEXJghitZnBqt01RTZl5Z7ddhthGvPhjFBwFncOQwF2aUpzHwwMQ07b21WW/iJL7mFSm2ouvhIkUkbFpMSaMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T12:41:20.680527Z"},"content_sha256":"829954b6eb0037520e41c00aa8e7adae293768deb648d80353c9d3874e8d7613","schema_version":"1.0","event_id":"sha256:829954b6eb0037520e41c00aa8e7adae293768deb648d80353c9d3874e8d7613"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/52RNVKU4BE6JMM5TFGTYT3CKO5/bundle.json","state_url":"https://pith.science/pith/52RNVKU4BE6JMM5TFGTYT3CKO5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/52RNVKU4BE6JMM5TFGTYT3CKO5/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":"2026-08-03T12:41:20Z","links":{"resolver":"https://pith.science/pith/52RNVKU4BE6JMM5TFGTYT3CKO5","bundle":"https://pith.science/pith/52RNVKU4BE6JMM5TFGTYT3CKO5/bundle.json","state":"https://pith.science/pith/52RNVKU4BE6JMM5TFGTYT3CKO5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/52RNVKU4BE6JMM5TFGTYT3CKO5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:52RNVKU4BE6JMM5TFGTYT3CKO5","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":"cf1e35ef558038a99b9b31feba3e74becb8f74681832bad18a94c5e2b49821d6","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"astro-ph","submitted_at":"2008-01-09T19:02:58Z","title_canon_sha256":"937a7aee08a44f5207c8c1289bf39c4ca181bbfebb2a6daf572f195409001490"},"schema_version":"1.0","source":{"id":"0801.1363","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1363","created_at":"2026-07-04T15:30:52Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1363v2","created_at":"2026-07-04T15:30:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1363","created_at":"2026-07-04T15:30:52Z"},{"alias_kind":"pith_short_12","alias_value":"52RNVKU4BE6J","created_at":"2026-07-04T15:30:52Z"},{"alias_kind":"pith_short_16","alias_value":"52RNVKU4BE6JMM5T","created_at":"2026-07-04T15:30:52Z"},{"alias_kind":"pith_short_8","alias_value":"52RNVKU4","created_at":"2026-07-04T15:30:52Z"}],"graph_snapshots":[{"event_id":"sha256:829954b6eb0037520e41c00aa8e7adae293768deb648d80353c9d3874e8d7613","target":"graph","created_at":"2026-07-04T15:30:52Z","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/0801.1363/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a framework for studying collective three-flavor neutrino oscillations based on the density matrix formalism. We show how techniques proven useful for collective two-flavor neutrino oscillations such as corotating frames can be applied readily to three-flavor mixing. Applying two simple assumptions and the conservation of two ``lepton numbers'' we use this framework to demonstrate how the adiabatic/precession solution emerges. We illustrate with a numerical example how two stepwise spectral swaps appear naturally if the flavor evolution of the neutrino gas can be described by such a","authors_text":"George M. Fuller, Huaiyu Duan, Yong-Zhong Qian","cross_cats":["hep-ph"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2008-01-09T19:02:58Z","title":"Stepwise Spectral Swapping with Three Neutrino Flavors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1363","kind":"arxiv","version":2},"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":"sha256:57c58dde84914d0531de37bbfe9a038d51f1c725c83030135e513759c9cf42d5","target":"record","created_at":"2026-07-04T15:30:52Z","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":"cf1e35ef558038a99b9b31feba3e74becb8f74681832bad18a94c5e2b49821d6","cross_cats_sorted":["hep-ph"],"license":"","primary_cat":"astro-ph","submitted_at":"2008-01-09T19:02:58Z","title_canon_sha256":"937a7aee08a44f5207c8c1289bf39c4ca181bbfebb2a6daf572f195409001490"},"schema_version":"1.0","source":{"id":"0801.1363","kind":"arxiv","version":2}},"canonical_sha256":"eea2daaa9c093c9633b329a789ec4a7748cfec8641183effd7bcf237235e4e3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eea2daaa9c093c9633b329a789ec4a7748cfec8641183effd7bcf237235e4e3d","first_computed_at":"2026-07-04T15:30:52.856251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:30:52.856251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LmHL++ilXWV7KethMg+MzbAy8dyz0G4zmGC38tfX9ZrADxLJ5hLfke65GNtH1qDLI78aElVS5EdMiJ/+yPukCg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:30:52.856629Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.1363","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57c58dde84914d0531de37bbfe9a038d51f1c725c83030135e513759c9cf42d5","sha256:829954b6eb0037520e41c00aa8e7adae293768deb648d80353c9d3874e8d7613"],"state_sha256":"cbdaa2ec93a42d6d1724b69c9b2fde96171af54af557b8fb0c035b0a25e44b7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hDgm9FMmYlXAvCeClmQEzTOQs8ttQ0mHBzDTBzCmPFhdsETNTKwWwnfxhFoDmB/ikpNSdAbu4ZUFEwMCRImaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T12:41:20.688899Z","bundle_sha256":"9c61fb26831a06bf91981accb1cdaf3fba3ceec3bda06be2de719ba3ef001a03"}}