{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MINTXK5DSGKA3FQUJ5PRGHAZNL","short_pith_number":"pith:MINTXK5D","schema_version":"1.0","canonical_sha256":"621b3baba391940d96144f5f131c196ac14a0ce4a18fab1e954e33d8b0f0d8f3","source":{"kind":"arxiv","id":"1507.01235","version":1},"attestation_state":"computed","paper":{"title":"Generalized $\\mu$-$\\tau$ symmetry and discrete subgroups of O(3)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Anjan S. Joshipura, Ketan M. Patel","submitted_at":"2015-07-05T16:11:11Z","abstract_excerpt":"The generalized $\\mu$-$\\tau$ interchange symmetry in the leptonic mixing matrix $U$ corresponds to the relations: $|U_{\\mu i}|=|U_{\\tau i}|$ with $i=1,2,3$. It predicts maximal atmospheric mixing and maximal Dirac CP violation given $\\theta_{13} \\neq 0$. We show that the generalized $\\mu$-$\\tau$ symmetry can arise if the charged lepton and neutrino mass matrices are invariant under specific residual symmetries contained in the finite discrete subgroups of $O(3)$. The groups $A_4$, $S_4$ and $A_5$ are the only such groups which can entirely fix $U$ at the leading order. The neutrinos can be (a)"},"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":"1507.01235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-07-05T16:11:11Z","cross_cats_sorted":[],"title_canon_sha256":"bfa687aeab189ccaa497fadafb527c8d608e0a455dc5da3e8483a09b99e0f140","abstract_canon_sha256":"4f9bbf34ae14bc49087fc33e8c956443b9ab161bb639176d62f235bfecf45110"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:39.656706Z","signature_b64":"v0WCyi3fs8XMW0T0ptZg7T210BpiuqK+zCt69a2Bt8o5w8+J3s/JrTQ3w59wWLITtGIyqYlsA5h8vVMX4WG6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"621b3baba391940d96144f5f131c196ac14a0ce4a18fab1e954e33d8b0f0d8f3","last_reissued_at":"2026-05-18T01:35:39.656088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:39.656088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized $\\mu$-$\\tau$ symmetry and discrete subgroups of O(3)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Anjan S. Joshipura, Ketan M. Patel","submitted_at":"2015-07-05T16:11:11Z","abstract_excerpt":"The generalized $\\mu$-$\\tau$ interchange symmetry in the leptonic mixing matrix $U$ corresponds to the relations: $|U_{\\mu i}|=|U_{\\tau i}|$ with $i=1,2,3$. It predicts maximal atmospheric mixing and maximal Dirac CP violation given $\\theta_{13} \\neq 0$. We show that the generalized $\\mu$-$\\tau$ symmetry can arise if the charged lepton and neutrino mass matrices are invariant under specific residual symmetries contained in the finite discrete subgroups of $O(3)$. The groups $A_4$, $S_4$ and $A_5$ are the only such groups which can entirely fix $U$ at the leading order. The neutrinos can be (a)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01235","kind":"arxiv","version":1},"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":"1507.01235","created_at":"2026-05-18T01:35:39.656184+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.01235v1","created_at":"2026-05-18T01:35:39.656184+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01235","created_at":"2026-05-18T01:35:39.656184+00:00"},{"alias_kind":"pith_short_12","alias_value":"MINTXK5DSGKA","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MINTXK5DSGKA3FQU","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MINTXK5D","created_at":"2026-05-18T12:29:32.376354+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/MINTXK5DSGKA3FQUJ5PRGHAZNL","json":"https://pith.science/pith/MINTXK5DSGKA3FQUJ5PRGHAZNL.json","graph_json":"https://pith.science/api/pith-number/MINTXK5DSGKA3FQUJ5PRGHAZNL/graph.json","events_json":"https://pith.science/api/pith-number/MINTXK5DSGKA3FQUJ5PRGHAZNL/events.json","paper":"https://pith.science/paper/MINTXK5D"},"agent_actions":{"view_html":"https://pith.science/pith/MINTXK5DSGKA3FQUJ5PRGHAZNL","download_json":"https://pith.science/pith/MINTXK5DSGKA3FQUJ5PRGHAZNL.json","view_paper":"https://pith.science/paper/MINTXK5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.01235&json=true","fetch_graph":"https://pith.science/api/pith-number/MINTXK5DSGKA3FQUJ5PRGHAZNL/graph.json","fetch_events":"https://pith.science/api/pith-number/MINTXK5DSGKA3FQUJ5PRGHAZNL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MINTXK5DSGKA3FQUJ5PRGHAZNL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MINTXK5DSGKA3FQUJ5PRGHAZNL/action/storage_attestation","attest_author":"https://pith.science/pith/MINTXK5DSGKA3FQUJ5PRGHAZNL/action/author_attestation","sign_citation":"https://pith.science/pith/MINTXK5DSGKA3FQUJ5PRGHAZNL/action/citation_signature","submit_replication":"https://pith.science/pith/MINTXK5DSGKA3FQUJ5PRGHAZNL/action/replication_record"}},"created_at":"2026-05-18T01:35:39.656184+00:00","updated_at":"2026-05-18T01:35:39.656184+00:00"}