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We prove that any such $V$ may be written in the form $V = U R P$, where $U$ is any predefined unitary matrix satisfying $S U = U^\\ast$, $R$ is an orthogonal, i.e. real, matrix, and $P$ is a diagonal matrix satisfying $P^2 = \\mathcal{P}$. Using this theorem, we demonstrate the equiv"},"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":"1708.09809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2017-08-31T16:40:54Z","cross_cats_sorted":[],"title_canon_sha256":"fd043123946833e3b5a2aa54f60f7e256a0e8917dc17e3cf9f34a6512f29960b","abstract_canon_sha256":"122b096d5e36de41016853207597cd7e055b3c4e9e7a8feb8b2295d3a7543ef8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:00.229078Z","signature_b64":"rJ58xDxbFD2c/W4P3/I9Q+9KTt5O8+2OMQTM/ZFPQoojrAvSADKDwO9QEVmLCnpPR36p/jOzriCLszYiEA0DBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"558ca4a80abb149f69f83403abe12c865ab5de4a6e80e61f2c2d01df30be350a","last_reissued_at":"2026-05-18T00:30:00.228659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:00.228659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cobimaximal lepton mixing from soft symmetry breaking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"L. Lavoura, W. Grimus","submitted_at":"2017-08-31T16:40:54Z","abstract_excerpt":"Cobimaximal lepton mixing, i.e. $\\theta_{23} = 45^\\circ$ and $\\delta = \\pm 90^\\circ$ in the lepton mixing matrix $V$, arises as a consequence of $S V = V^\\ast \\mathcal{P}$, where $S$ is the permutation matrix that interchanges the second and third rows of $V$ and $\\mathcal{P}$ is a diagonal matrix of phase factors. We prove that any such $V$ may be written in the form $V = U R P$, where $U$ is any predefined unitary matrix satisfying $S U = U^\\ast$, $R$ is an orthogonal, i.e. real, matrix, and $P$ is a diagonal matrix satisfying $P^2 = \\mathcal{P}$. Using this theorem, we demonstrate the equiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09809","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":"1708.09809","created_at":"2026-05-18T00:30:00.228718+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.09809v1","created_at":"2026-05-18T00:30:00.228718+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09809","created_at":"2026-05-18T00:30:00.228718+00:00"},{"alias_kind":"pith_short_12","alias_value":"KWGKJKAKXMKJ","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"KWGKJKAKXMKJ62PY","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"KWGKJKAK","created_at":"2026-05-18T12:31:28.150371+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/KWGKJKAKXMKJ62PYGQB2XYJMQZ","json":"https://pith.science/pith/KWGKJKAKXMKJ62PYGQB2XYJMQZ.json","graph_json":"https://pith.science/api/pith-number/KWGKJKAKXMKJ62PYGQB2XYJMQZ/graph.json","events_json":"https://pith.science/api/pith-number/KWGKJKAKXMKJ62PYGQB2XYJMQZ/events.json","paper":"https://pith.science/paper/KWGKJKAK"},"agent_actions":{"view_html":"https://pith.science/pith/KWGKJKAKXMKJ62PYGQB2XYJMQZ","download_json":"https://pith.science/pith/KWGKJKAKXMKJ62PYGQB2XYJMQZ.json","view_paper":"https://pith.science/paper/KWGKJKAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.09809&json=true","fetch_graph":"https://pith.science/api/pith-number/KWGKJKAKXMKJ62PYGQB2XYJMQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/KWGKJKAKXMKJ62PYGQB2XYJMQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KWGKJKAKXMKJ62PYGQB2XYJMQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KWGKJKAKXMKJ62PYGQB2XYJMQZ/action/storage_attestation","attest_author":"https://pith.science/pith/KWGKJKAKXMKJ62PYGQB2XYJMQZ/action/author_attestation","sign_citation":"https://pith.science/pith/KWGKJKAKXMKJ62PYGQB2XYJMQZ/action/citation_signature","submit_replication":"https://pith.science/pith/KWGKJKAKXMKJ62PYGQB2XYJMQZ/action/replication_record"}},"created_at":"2026-05-18T00:30:00.228718+00:00","updated_at":"2026-05-18T00:30:00.228718+00:00"}