{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7ORHG27XTN7WK4RKR7QMSHD3RO","short_pith_number":"pith:7ORHG27X","canonical_record":{"source":{"id":"1105.1182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-05T22:09:31Z","cross_cats_sorted":["hep-ph","math-ph","math.MP","nucl-th"],"title_canon_sha256":"c786ec72175e53fd7de2537bb702097701b3816b7289b5eef11c984601f68308","abstract_canon_sha256":"1c1250ebbadd6563187dc30322ba6d5d9f2a8632aba15f4e8ee1d969e148b747"},"schema_version":"1.0"},"canonical_sha256":"fba2736bf79b7f65722a8fe0c91c7b8bbbb6fd2ea948eeb2241a053996ce9527","source":{"kind":"arxiv","id":"1105.1182","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1182","created_at":"2026-05-18T02:02:03Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1182v2","created_at":"2026-05-18T02:02:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1182","created_at":"2026-05-18T02:02:03Z"},{"alias_kind":"pith_short_12","alias_value":"7ORHG27XTN7W","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7ORHG27XTN7WK4RK","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7ORHG27X","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7ORHG27XTN7WK4RKR7QMSHD3RO","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-05T22:09:31Z","cross_cats_sorted":["hep-ph","math-ph","math.MP","nucl-th"],"title_canon_sha256":"c786ec72175e53fd7de2537bb702097701b3816b7289b5eef11c984601f68308","abstract_canon_sha256":"1c1250ebbadd6563187dc30322ba6d5d9f2a8632aba15f4e8ee1d969e148b747"},"schema_version":"1.0"},"canonical_sha256":"fba2736bf79b7f65722a8fe0c91c7b8bbbb6fd2ea948eeb2241a053996ce9527","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:03.572537Z","signature_b64":"+Mqacln1cRoIy6swPrEImP6wZyU8jEKwq8VxnPuyPBBllwEp2zBRzAPThLlnYjiKODV9GEyGomuwl1aldPjNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fba2736bf79b7f65722a8fe0c91c7b8bbbb6fd2ea948eeb2241a053996ce9527","last_reissued_at":"2026-05-18T02:02:03.572004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:03.572004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1182","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":"2026-05-18T02:02:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YTAeXsB0S08X+zopcf+b4ox31EyHOhfV+GCVc6TKPxit3uRJRspoivL9cxVZzHaruIiBVHSBNW+g8Ygo7gUwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:17:33.430921Z"},"content_sha256":"ed7a8e27b8923cd8758ac6ce5544ea3827f4aece84254360e01672e72876c941","schema_version":"1.0","event_id":"sha256:ed7a8e27b8923cd8758ac6ce5544ea3827f4aece84254360e01672e72876c941"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7ORHG27XTN7WK4RKR7QMSHD3RO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants of Collective Neutrino Oscillations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP","nucl-th"],"primary_cat":"astro-ph.CO","authors_text":"A. B. Balantekin, Takashi Yoshida, Toshitaka Kajino, Y. Pehlivan","submitted_at":"2011-05-05T22:09:31Z","abstract_excerpt":"We consider the flavor evolution of a dense neutrino gas by taking into account both vacuum oscillations and self interactions of neutrinos. We examine the system from a many-body perspective as well as from the point of view of an effective one-body description formulated in terms of the neutrino polarization vectors. We show that, in the single angle approximation, both the many-body picture and the effective one-particle picture possess several constants of motion. We write down these constants of motion explicitly in terms of the neutrino isospin operators for the many-body case and in ter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1182","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":""},"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":"2026-05-18T02:02:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kGr0vpWlMwaqNyDVVcF88Gr6/n8ggoB+ce1vCW2SF5wlfyjU5xDKBbZ4IFGtYUAGVZDZrK74ydynNAXDrDXlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:17:33.431567Z"},"content_sha256":"5fec6d7de543827a99e40ad09e133a6ad491ac2c11a58f4211e19a8e5c05061a","schema_version":"1.0","event_id":"sha256:5fec6d7de543827a99e40ad09e133a6ad491ac2c11a58f4211e19a8e5c05061a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ORHG27XTN7WK4RKR7QMSHD3RO/bundle.json","state_url":"https://pith.science/pith/7ORHG27XTN7WK4RKR7QMSHD3RO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ORHG27XTN7WK4RKR7QMSHD3RO/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":"2026-05-25T18:17:33Z","links":{"resolver":"https://pith.science/pith/7ORHG27XTN7WK4RKR7QMSHD3RO","bundle":"https://pith.science/pith/7ORHG27XTN7WK4RKR7QMSHD3RO/bundle.json","state":"https://pith.science/pith/7ORHG27XTN7WK4RKR7QMSHD3RO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ORHG27XTN7WK4RKR7QMSHD3RO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7ORHG27XTN7WK4RKR7QMSHD3RO","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":"1c1250ebbadd6563187dc30322ba6d5d9f2a8632aba15f4e8ee1d969e148b747","cross_cats_sorted":["hep-ph","math-ph","math.MP","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-05T22:09:31Z","title_canon_sha256":"c786ec72175e53fd7de2537bb702097701b3816b7289b5eef11c984601f68308"},"schema_version":"1.0","source":{"id":"1105.1182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1182","created_at":"2026-05-18T02:02:03Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1182v2","created_at":"2026-05-18T02:02:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1182","created_at":"2026-05-18T02:02:03Z"},{"alias_kind":"pith_short_12","alias_value":"7ORHG27XTN7W","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7ORHG27XTN7WK4RK","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7ORHG27X","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:5fec6d7de543827a99e40ad09e133a6ad491ac2c11a58f4211e19a8e5c05061a","target":"graph","created_at":"2026-05-18T02:02:03Z","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":"We consider the flavor evolution of a dense neutrino gas by taking into account both vacuum oscillations and self interactions of neutrinos. We examine the system from a many-body perspective as well as from the point of view of an effective one-body description formulated in terms of the neutrino polarization vectors. We show that, in the single angle approximation, both the many-body picture and the effective one-particle picture possess several constants of motion. We write down these constants of motion explicitly in terms of the neutrino isospin operators for the many-body case and in ter","authors_text":"A. B. Balantekin, Takashi Yoshida, Toshitaka Kajino, Y. Pehlivan","cross_cats":["hep-ph","math-ph","math.MP","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-05T22:09:31Z","title":"Invariants of Collective Neutrino Oscillations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1182","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:ed7a8e27b8923cd8758ac6ce5544ea3827f4aece84254360e01672e72876c941","target":"record","created_at":"2026-05-18T02:02:03Z","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":"1c1250ebbadd6563187dc30322ba6d5d9f2a8632aba15f4e8ee1d969e148b747","cross_cats_sorted":["hep-ph","math-ph","math.MP","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-05T22:09:31Z","title_canon_sha256":"c786ec72175e53fd7de2537bb702097701b3816b7289b5eef11c984601f68308"},"schema_version":"1.0","source":{"id":"1105.1182","kind":"arxiv","version":2}},"canonical_sha256":"fba2736bf79b7f65722a8fe0c91c7b8bbbb6fd2ea948eeb2241a053996ce9527","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fba2736bf79b7f65722a8fe0c91c7b8bbbb6fd2ea948eeb2241a053996ce9527","first_computed_at":"2026-05-18T02:02:03.572004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:03.572004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Mqacln1cRoIy6swPrEImP6wZyU8jEKwq8VxnPuyPBBllwEp2zBRzAPThLlnYjiKODV9GEyGomuwl1aldPjNBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:03.572537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed7a8e27b8923cd8758ac6ce5544ea3827f4aece84254360e01672e72876c941","sha256:5fec6d7de543827a99e40ad09e133a6ad491ac2c11a58f4211e19a8e5c05061a"],"state_sha256":"b79dedc8d1101944d7e743358fc68fa3f2958e91ee9b23329cf86e65ac0bb10a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"68rs8nLsrQFaexBnCt0ubX366iQFPfdTefGiQzThhjukoyWv38XWNJimq/iY+K2Y6y3xCt++RMGu8VGs/qDnAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:17:33.434876Z","bundle_sha256":"8754359b934dd1149988dc7b8f9cabb37323b33b5fa73989a5d3b489c5c590ad"}}