{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:HRWFE3W2BYGIORR2HUWIP7DSW6","short_pith_number":"pith:HRWFE3W2","schema_version":"1.0","canonical_sha256":"3c6c526eda0e0c87463a3d2c87fc72b784276cf626d502705b52c4ce52511a55","source":{"kind":"arxiv","id":"1012.4886","version":3},"attestation_state":"computed","paper":{"title":"Phenomenology in the Zee Model with the A_4 Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Hiroaki Sugiyama (Ritsumeikan U., Koji Tsumura (Natl. Taiwan U., Kusatsu), Kusatsu & Kyoto sangyo U., Kyoto), Taipei), Takeshi Fukuyama (Ritsumeikan U.","submitted_at":"2010-12-22T06:43:41Z","abstract_excerpt":"The Zee model generates neutrino masses at the one-loop level by adding charged SU(2)_L-singlet and extra SU(2)_L-doublet scalars to the standard model of particle physics. As the origin of the nontrivial structure of the lepton flavor mixing, we introduce the softly broken A_4 symmetry to the Zee model. This model is compatible with the tribimaximal mixing which agrees well with neutrino oscillation measurements. Then, a sum rule m_1 e^{i alpha_12} + 2 m_2 + 3 m_3 e^{i alpha_32} = 0 is obtained and it results in Delta m^2_31 < 0 and m_3 > 1.8*10^{-2}eV. The effective mass |(M_nu)_{ee}| for th"},"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":"1012.4886","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-12-22T06:43:41Z","cross_cats_sorted":[],"title_canon_sha256":"09bfd9ffce8558342402f0d37b3503f7983adfc2f2d798100941dbf7ea8af092","abstract_canon_sha256":"7fa85dc873e975e634407b6e1d5adf8e2748e554bee6bd898fdd3103aec9d1a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:06.618712Z","signature_b64":"5O4LfLOfF681eE2PDVaOXHU4wOSYn9vDxQSwNBhSr/XlLFzdktX5dpPBEEyzfGkL/ig6pVNfoJFmEUtdoPPxCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c6c526eda0e0c87463a3d2c87fc72b784276cf626d502705b52c4ce52511a55","last_reissued_at":"2026-05-18T02:23:06.618205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:06.618205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phenomenology in the Zee Model with the A_4 Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Hiroaki Sugiyama (Ritsumeikan U., Koji Tsumura (Natl. Taiwan U., Kusatsu), Kusatsu & Kyoto sangyo U., Kyoto), Taipei), Takeshi Fukuyama (Ritsumeikan U.","submitted_at":"2010-12-22T06:43:41Z","abstract_excerpt":"The Zee model generates neutrino masses at the one-loop level by adding charged SU(2)_L-singlet and extra SU(2)_L-doublet scalars to the standard model of particle physics. As the origin of the nontrivial structure of the lepton flavor mixing, we introduce the softly broken A_4 symmetry to the Zee model. This model is compatible with the tribimaximal mixing which agrees well with neutrino oscillation measurements. Then, a sum rule m_1 e^{i alpha_12} + 2 m_2 + 3 m_3 e^{i alpha_32} = 0 is obtained and it results in Delta m^2_31 < 0 and m_3 > 1.8*10^{-2}eV. The effective mass |(M_nu)_{ee}| for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4886","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":""},"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":"1012.4886","created_at":"2026-05-18T02:23:06.618287+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.4886v3","created_at":"2026-05-18T02:23:06.618287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4886","created_at":"2026-05-18T02:23:06.618287+00:00"},{"alias_kind":"pith_short_12","alias_value":"HRWFE3W2BYGI","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"HRWFE3W2BYGIORR2","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"HRWFE3W2","created_at":"2026-05-18T12:26:07.630475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.23202","citing_title":"Zee models with a non-invertible $Z_M$ symmetry","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HRWFE3W2BYGIORR2HUWIP7DSW6","json":"https://pith.science/pith/HRWFE3W2BYGIORR2HUWIP7DSW6.json","graph_json":"https://pith.science/api/pith-number/HRWFE3W2BYGIORR2HUWIP7DSW6/graph.json","events_json":"https://pith.science/api/pith-number/HRWFE3W2BYGIORR2HUWIP7DSW6/events.json","paper":"https://pith.science/paper/HRWFE3W2"},"agent_actions":{"view_html":"https://pith.science/pith/HRWFE3W2BYGIORR2HUWIP7DSW6","download_json":"https://pith.science/pith/HRWFE3W2BYGIORR2HUWIP7DSW6.json","view_paper":"https://pith.science/paper/HRWFE3W2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.4886&json=true","fetch_graph":"https://pith.science/api/pith-number/HRWFE3W2BYGIORR2HUWIP7DSW6/graph.json","fetch_events":"https://pith.science/api/pith-number/HRWFE3W2BYGIORR2HUWIP7DSW6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HRWFE3W2BYGIORR2HUWIP7DSW6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HRWFE3W2BYGIORR2HUWIP7DSW6/action/storage_attestation","attest_author":"https://pith.science/pith/HRWFE3W2BYGIORR2HUWIP7DSW6/action/author_attestation","sign_citation":"https://pith.science/pith/HRWFE3W2BYGIORR2HUWIP7DSW6/action/citation_signature","submit_replication":"https://pith.science/pith/HRWFE3W2BYGIORR2HUWIP7DSW6/action/replication_record"}},"created_at":"2026-05-18T02:23:06.618287+00:00","updated_at":"2026-05-18T02:23:06.618287+00:00"}