{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GCB5NIFB7SUWQTE4DUBOERIB3O","short_pith_number":"pith:GCB5NIFB","canonical_record":{"source":{"id":"1103.2891","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-03-15T12:20:37Z","cross_cats_sorted":["astro-ph.SR"],"title_canon_sha256":"47566bd58017d4c59df94271c7673e2540e873b6147c93d57e8bea76d3b329eb","abstract_canon_sha256":"491de6c657091441a93d68a3c9afb39c8de06f1669bd029ac5283550a1ad7680"},"schema_version":"1.0"},"canonical_sha256":"3083d6a0a1fca9684c9c1d02e24501db9b5ca1e0952f689cfa6f9a747f2360d8","source":{"kind":"arxiv","id":"1103.2891","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2891","created_at":"2026-07-05T03:13:18Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2891v4","created_at":"2026-07-05T03:13:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2891","created_at":"2026-07-05T03:13:18Z"},{"alias_kind":"pith_short_12","alias_value":"GCB5NIFB7SUW","created_at":"2026-07-05T03:13:18Z"},{"alias_kind":"pith_short_16","alias_value":"GCB5NIFB7SUWQTE4","created_at":"2026-07-05T03:13:18Z"},{"alias_kind":"pith_short_8","alias_value":"GCB5NIFB","created_at":"2026-07-05T03:13:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GCB5NIFB7SUWQTE4DUBOERIB3O","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2891","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-03-15T12:20:37Z","cross_cats_sorted":["astro-ph.SR"],"title_canon_sha256":"47566bd58017d4c59df94271c7673e2540e873b6147c93d57e8bea76d3b329eb","abstract_canon_sha256":"491de6c657091441a93d68a3c9afb39c8de06f1669bd029ac5283550a1ad7680"},"schema_version":"1.0"},"canonical_sha256":"3083d6a0a1fca9684c9c1d02e24501db9b5ca1e0952f689cfa6f9a747f2360d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:13:18.543803Z","signature_b64":"iMbYWn0m+ZLVzE81WmMkrJB6hK9SMfguyStkPj6lxTA6j4PdvqwuyggExJu0Il/OHKhU2CnJeZtlC/jqyqLjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3083d6a0a1fca9684c9c1d02e24501db9b5ca1e0952f689cfa6f9a747f2360d8","last_reissued_at":"2026-07-05T03:13:18.543335Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:13:18.543335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2891","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:13:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6VGY5sCA8yO2f2IxNJCoLQUm11ueSHkF1wCOtsapIaswrOsLqaEFhnCRekwAea0ELI/lMXVwlVkU5I5WagcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T17:55:22.977521Z"},"content_sha256":"5566c5688942f531c710a197fd7e722f916df4e0563bc142506f9a1f22fcc45e","schema_version":"1.0","event_id":"sha256:5566c5688942f531c710a197fd7e722f916df4e0563bc142506f9a1f22fcc45e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GCB5NIFB7SUWQTE4DUBOERIB3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"N-mode coherence in collective neutrino oscillations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.SR"],"primary_cat":"hep-ph","authors_text":"Georg G. Raffelt","submitted_at":"2011-03-15T12:20:37Z","abstract_excerpt":"We study two-flavor neutrino oscillations in a homogeneous and isotropic ensemble under the influence of neutrino-neutrino interactions. For any density there exist forms of collective oscillations that show self-maintained coherence. They can be classified by a number N of linearly independent functions that describe all neutrino modes as linear superpositions. What is more, the dynamics is equivalent to another ensemble with the same effective density, consisting of N modes with discrete energies E_i with i=1, ..., N. We use this equivalence to derive the analytic solution for two-mode (bimo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2891","kind":"arxiv","version":4},"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/1103.2891/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":"2026-07-05T03:13:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3VU6o8qoGfBPKBtEnVtAHE6rdc38XNhiL5Tn3/3ZYCp68lRGyAYTMT59nlEXfDgM5yh9/BY7vqe9JopB2sr3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T17:55:22.978216Z"},"content_sha256":"60f35fb6d2e585aa1f2003d550e4bc346bf879127b04f48dfedf73a7e90bdd77","schema_version":"1.0","event_id":"sha256:60f35fb6d2e585aa1f2003d550e4bc346bf879127b04f48dfedf73a7e90bdd77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCB5NIFB7SUWQTE4DUBOERIB3O/bundle.json","state_url":"https://pith.science/pith/GCB5NIFB7SUWQTE4DUBOERIB3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCB5NIFB7SUWQTE4DUBOERIB3O/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":"2026-08-12T17:55:22Z","links":{"resolver":"https://pith.science/pith/GCB5NIFB7SUWQTE4DUBOERIB3O","bundle":"https://pith.science/pith/GCB5NIFB7SUWQTE4DUBOERIB3O/bundle.json","state":"https://pith.science/pith/GCB5NIFB7SUWQTE4DUBOERIB3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCB5NIFB7SUWQTE4DUBOERIB3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GCB5NIFB7SUWQTE4DUBOERIB3O","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":"491de6c657091441a93d68a3c9afb39c8de06f1669bd029ac5283550a1ad7680","cross_cats_sorted":["astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-03-15T12:20:37Z","title_canon_sha256":"47566bd58017d4c59df94271c7673e2540e873b6147c93d57e8bea76d3b329eb"},"schema_version":"1.0","source":{"id":"1103.2891","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2891","created_at":"2026-07-05T03:13:18Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2891v4","created_at":"2026-07-05T03:13:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2891","created_at":"2026-07-05T03:13:18Z"},{"alias_kind":"pith_short_12","alias_value":"GCB5NIFB7SUW","created_at":"2026-07-05T03:13:18Z"},{"alias_kind":"pith_short_16","alias_value":"GCB5NIFB7SUWQTE4","created_at":"2026-07-05T03:13:18Z"},{"alias_kind":"pith_short_8","alias_value":"GCB5NIFB","created_at":"2026-07-05T03:13:18Z"}],"graph_snapshots":[{"event_id":"sha256:60f35fb6d2e585aa1f2003d550e4bc346bf879127b04f48dfedf73a7e90bdd77","target":"graph","created_at":"2026-07-05T03:13:18Z","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/1103.2891/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study two-flavor neutrino oscillations in a homogeneous and isotropic ensemble under the influence of neutrino-neutrino interactions. For any density there exist forms of collective oscillations that show self-maintained coherence. They can be classified by a number N of linearly independent functions that describe all neutrino modes as linear superpositions. What is more, the dynamics is equivalent to another ensemble with the same effective density, consisting of N modes with discrete energies E_i with i=1, ..., N. We use this equivalence to derive the analytic solution for two-mode (bimo","authors_text":"Georg G. Raffelt","cross_cats":["astro-ph.SR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-03-15T12:20:37Z","title":"N-mode coherence in collective neutrino oscillations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2891","kind":"arxiv","version":4},"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":"sha256:5566c5688942f531c710a197fd7e722f916df4e0563bc142506f9a1f22fcc45e","target":"record","created_at":"2026-07-05T03:13:18Z","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":"491de6c657091441a93d68a3c9afb39c8de06f1669bd029ac5283550a1ad7680","cross_cats_sorted":["astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-03-15T12:20:37Z","title_canon_sha256":"47566bd58017d4c59df94271c7673e2540e873b6147c93d57e8bea76d3b329eb"},"schema_version":"1.0","source":{"id":"1103.2891","kind":"arxiv","version":4}},"canonical_sha256":"3083d6a0a1fca9684c9c1d02e24501db9b5ca1e0952f689cfa6f9a747f2360d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3083d6a0a1fca9684c9c1d02e24501db9b5ca1e0952f689cfa6f9a747f2360d8","first_computed_at":"2026-07-05T03:13:18.543335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:13:18.543335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iMbYWn0m+ZLVzE81WmMkrJB6hK9SMfguyStkPj6lxTA6j4PdvqwuyggExJu0Il/OHKhU2CnJeZtlC/jqyqLjBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:13:18.543803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2891","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5566c5688942f531c710a197fd7e722f916df4e0563bc142506f9a1f22fcc45e","sha256:60f35fb6d2e585aa1f2003d550e4bc346bf879127b04f48dfedf73a7e90bdd77"],"state_sha256":"04161b7a947ab5b6f2e2176ab3959840c5cd3b24d447a25189a262b80e0a2723"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mzQTUBBYCaH1To3XOZQSwKi94T2UIw2D0oYw0q9QXecsgdkK3Cxi6tXvzsTHsS/iOA5KoPGElUGtAaqn/w8+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T17:55:22.984783Z","bundle_sha256":"c53cac950b46e03b429eaf2bb70b8053d8e8e99cea8fbfb0e16735c23a598445"}}