{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:XXKBJC2RH45O6QMUYDRO3C6L6R","short_pith_number":"pith:XXKBJC2R","schema_version":"1.0","canonical_sha256":"bdd4148b513f3aef4194c0e2ed8bcbf454587bb7533ac4d795d3eae9bf055887","source":{"kind":"arxiv","id":"1109.4260","version":2},"attestation_state":"computed","paper":{"title":"Dirac Lepton Angle Matrix v.s. Majorana Lepton Angle Matrix and Their Renormalization Group Running Behaviours","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Shu Luo","submitted_at":"2011-09-20T10:38:37Z","abstract_excerpt":"Enlightened by the idea of the 3 times 3 CKM angle matrix proposed recently by Harrison et al., we introduce the Dirac angle matrix Phi and the Majorana angle matrix Psi in the lepton sector for Dirac and Majorana neutrinos respectively. We show that in presence of the CP violation, the angle matrix Phi or Psi is entirely equivalent to the complex MNS matrix V itself, but has the advantage of being real, phase rephasing invariant, directly associated to the leptonic unitarity triangles (UTs) and do not depend on any particular parametrization of V. In this paper, we further analyzed how the an"},"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":"1109.4260","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-09-20T10:38:37Z","cross_cats_sorted":[],"title_canon_sha256":"b19770b9fbaed9dee6d3a329c2063fde35e5686eb036aa5da0ec7f14d7bb7d24","abstract_canon_sha256":"944dad4de2e81cda2cc2646c3f5b3442129abdbd5ca66d8d1e09532c08fb9877"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:28.819067Z","signature_b64":"Mk/dVCArpGUeGnSYDjTW3sXmYeVgEDRa92d5Yn9LAdOcduZSljyk2FVaRT6U1P7DOwnvv1hxAlbvdH1YYMsgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdd4148b513f3aef4194c0e2ed8bcbf454587bb7533ac4d795d3eae9bf055887","last_reissued_at":"2026-05-18T02:00:28.818484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:28.818484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dirac Lepton Angle Matrix v.s. Majorana Lepton Angle Matrix and Their Renormalization Group Running Behaviours","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Shu Luo","submitted_at":"2011-09-20T10:38:37Z","abstract_excerpt":"Enlightened by the idea of the 3 times 3 CKM angle matrix proposed recently by Harrison et al., we introduce the Dirac angle matrix Phi and the Majorana angle matrix Psi in the lepton sector for Dirac and Majorana neutrinos respectively. We show that in presence of the CP violation, the angle matrix Phi or Psi is entirely equivalent to the complex MNS matrix V itself, but has the advantage of being real, phase rephasing invariant, directly associated to the leptonic unitarity triangles (UTs) and do not depend on any particular parametrization of V. In this paper, we further analyzed how the an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4260","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.4260","created_at":"2026-05-18T02:00:28.818568+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.4260v2","created_at":"2026-05-18T02:00:28.818568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4260","created_at":"2026-05-18T02:00:28.818568+00:00"},{"alias_kind":"pith_short_12","alias_value":"XXKBJC2RH45O","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"XXKBJC2RH45O6QMU","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"XXKBJC2R","created_at":"2026-05-18T12:26:47.523578+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/XXKBJC2RH45O6QMUYDRO3C6L6R","json":"https://pith.science/pith/XXKBJC2RH45O6QMUYDRO3C6L6R.json","graph_json":"https://pith.science/api/pith-number/XXKBJC2RH45O6QMUYDRO3C6L6R/graph.json","events_json":"https://pith.science/api/pith-number/XXKBJC2RH45O6QMUYDRO3C6L6R/events.json","paper":"https://pith.science/paper/XXKBJC2R"},"agent_actions":{"view_html":"https://pith.science/pith/XXKBJC2RH45O6QMUYDRO3C6L6R","download_json":"https://pith.science/pith/XXKBJC2RH45O6QMUYDRO3C6L6R.json","view_paper":"https://pith.science/paper/XXKBJC2R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.4260&json=true","fetch_graph":"https://pith.science/api/pith-number/XXKBJC2RH45O6QMUYDRO3C6L6R/graph.json","fetch_events":"https://pith.science/api/pith-number/XXKBJC2RH45O6QMUYDRO3C6L6R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XXKBJC2RH45O6QMUYDRO3C6L6R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XXKBJC2RH45O6QMUYDRO3C6L6R/action/storage_attestation","attest_author":"https://pith.science/pith/XXKBJC2RH45O6QMUYDRO3C6L6R/action/author_attestation","sign_citation":"https://pith.science/pith/XXKBJC2RH45O6QMUYDRO3C6L6R/action/citation_signature","submit_replication":"https://pith.science/pith/XXKBJC2RH45O6QMUYDRO3C6L6R/action/replication_record"}},"created_at":"2026-05-18T02:00:28.818568+00:00","updated_at":"2026-05-18T02:00:28.818568+00:00"}