{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:QTDBN6NMKB3QRJQDFUTBSSWF3U","short_pith_number":"pith:QTDBN6NM","schema_version":"1.0","canonical_sha256":"84c616f9ac507708a6032d26194ac5dd2609bd17f16e940b2fd91cf3b72805f1","source":{"kind":"arxiv","id":"2009.12347","version":3},"attestation_state":"computed","paper":{"title":"Sufficient and Necessary Conditions for CP Conservation in the Case of Degenerate Majorana Neutrino Masses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Bingrong Yu, Shun Zhou","submitted_at":"2020-09-25T17:14:57Z","abstract_excerpt":"In this paper, we carry out a systematic study of the sufficient and necessary conditions for CP conservation in the leptonic sector with massive Majorana neutrinos. In particular, the emphasis is placed on the number of CP-violating phases in the presence of a partial mass degeneracy (e.g., $m^{}_1 = m^{}_2 \\neq m^{}_3$) or a complete mass degeneracy $m^{}_1 = m^{}_2 = m^{}_3$, where $m^{}_i$ (for $i = 1, 2, 3$) stand for the masses of three ordinary neutrinos. In the canonical seesaw model with three right-handed neutrino singlets, CP-violating phases in the special case of a partial (e.g., "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2009.12347","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-09-25T17:14:57Z","cross_cats_sorted":[],"title_canon_sha256":"296420b3a54cdec9c7680c2372333d8e4be1c2b14aee1bf912064337d3381811","abstract_canon_sha256":"f56915a4e2442622f474fd18a84a4cd91664f776a65b33b9b7bf4191c1e63be6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:16:49.218979Z","signature_b64":"tCPRSvxl3bn5nISyTNagbcJiSjP2LfU3Njv5/zFVerpGAWsdozz9/s34YF36yeTVIJldO+pd2BIUOsDX6rRvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84c616f9ac507708a6032d26194ac5dd2609bd17f16e940b2fd91cf3b72805f1","last_reissued_at":"2026-07-05T02:16:49.218582Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:16:49.218582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sufficient and Necessary Conditions for CP Conservation in the Case of Degenerate Majorana Neutrino Masses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Bingrong Yu, Shun Zhou","submitted_at":"2020-09-25T17:14:57Z","abstract_excerpt":"In this paper, we carry out a systematic study of the sufficient and necessary conditions for CP conservation in the leptonic sector with massive Majorana neutrinos. In particular, the emphasis is placed on the number of CP-violating phases in the presence of a partial mass degeneracy (e.g., $m^{}_1 = m^{}_2 \\neq m^{}_3$) or a complete mass degeneracy $m^{}_1 = m^{}_2 = m^{}_3$, where $m^{}_i$ (for $i = 1, 2, 3$) stand for the masses of three ordinary neutrinos. In the canonical seesaw model with three right-handed neutrino singlets, CP-violating phases in the special case of a partial (e.g., "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.12347","kind":"arxiv","version":3},"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/2009.12347/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2009.12347","created_at":"2026-07-05T02:16:49.218638+00:00"},{"alias_kind":"arxiv_version","alias_value":"2009.12347v3","created_at":"2026-07-05T02:16:49.218638+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.12347","created_at":"2026-07-05T02:16:49.218638+00:00"},{"alias_kind":"pith_short_12","alias_value":"QTDBN6NMKB3Q","created_at":"2026-07-05T02:16:49.218638+00:00"},{"alias_kind":"pith_short_16","alias_value":"QTDBN6NMKB3QRJQD","created_at":"2026-07-05T02:16:49.218638+00:00"},{"alias_kind":"pith_short_8","alias_value":"QTDBN6NM","created_at":"2026-07-05T02:16:49.218638+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QTDBN6NMKB3QRJQDFUTBSSWF3U","json":"https://pith.science/pith/QTDBN6NMKB3QRJQDFUTBSSWF3U.json","graph_json":"https://pith.science/api/pith-number/QTDBN6NMKB3QRJQDFUTBSSWF3U/graph.json","events_json":"https://pith.science/api/pith-number/QTDBN6NMKB3QRJQDFUTBSSWF3U/events.json","paper":"https://pith.science/paper/QTDBN6NM"},"agent_actions":{"view_html":"https://pith.science/pith/QTDBN6NMKB3QRJQDFUTBSSWF3U","download_json":"https://pith.science/pith/QTDBN6NMKB3QRJQDFUTBSSWF3U.json","view_paper":"https://pith.science/paper/QTDBN6NM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2009.12347&json=true","fetch_graph":"https://pith.science/api/pith-number/QTDBN6NMKB3QRJQDFUTBSSWF3U/graph.json","fetch_events":"https://pith.science/api/pith-number/QTDBN6NMKB3QRJQDFUTBSSWF3U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QTDBN6NMKB3QRJQDFUTBSSWF3U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QTDBN6NMKB3QRJQDFUTBSSWF3U/action/storage_attestation","attest_author":"https://pith.science/pith/QTDBN6NMKB3QRJQDFUTBSSWF3U/action/author_attestation","sign_citation":"https://pith.science/pith/QTDBN6NMKB3QRJQDFUTBSSWF3U/action/citation_signature","submit_replication":"https://pith.science/pith/QTDBN6NMKB3QRJQDFUTBSSWF3U/action/replication_record"}},"created_at":"2026-07-05T02:16:49.218638+00:00","updated_at":"2026-07-05T02:16:49.218638+00:00"}