{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7S762SNQAHA44CXFO4FJ5ASY5I","short_pith_number":"pith:7S762SNQ","schema_version":"1.0","canonical_sha256":"fcbfed49b001c1ce0ae5770a9e8258ea368b92925d68a837669641c9d049402d","source":{"kind":"arxiv","id":"1809.10292","version":2},"attestation_state":"computed","paper":{"title":"Spontaneous breaking of $SO(3)$ to finite family symmetries with supersymmetry - an $A_4$ model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Stephen F. King, Ye-Ling Zhou","submitted_at":"2018-09-27T01:12:43Z","abstract_excerpt":"We discuss the breaking of $SO(3)$ down to finite family symmetries such as $A_4$, $S_4$ and $A_5$ using supersymmetric potentials for the first time. We analyse in detail the case of supersymmetric $A_4$ and its finite subgroups $Z_3$ and $Z_2$. We then propose a supersymmetric $A_4$ model of leptons along these lines, originating from $SO(3)\\times U(1)$, which leads to a phenomenologically acceptable pattern of lepton mixing and masses once subleading corrections are taken into account. We also discuss the phenomenological consequences of having a gauged $SO(3)$, leading to massive gauge bos"},"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":"1809.10292","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-09-27T01:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"1dbb1d3c4fded3a892508499a996814c97ec421721f7e267c9ede2b34ce1b9a6","abstract_canon_sha256":"824baaf5b7698407677dbb0e0b974a3bae3fdaf1dd2d1677e5c64a55ed2d2dbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:30.467864Z","signature_b64":"gjkdN6/cPbkx/eYF6gvrCSnhFhbRYwtFU2JU3LHoAThubFYmfJj3z7UPVKED8QIy+kMQWQ9hCM8TAzu49GRcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcbfed49b001c1ce0ae5770a9e8258ea368b92925d68a837669641c9d049402d","last_reissued_at":"2026-05-17T23:58:30.467289Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:30.467289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spontaneous breaking of $SO(3)$ to finite family symmetries with supersymmetry - an $A_4$ model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Stephen F. King, Ye-Ling Zhou","submitted_at":"2018-09-27T01:12:43Z","abstract_excerpt":"We discuss the breaking of $SO(3)$ down to finite family symmetries such as $A_4$, $S_4$ and $A_5$ using supersymmetric potentials for the first time. We analyse in detail the case of supersymmetric $A_4$ and its finite subgroups $Z_3$ and $Z_2$. We then propose a supersymmetric $A_4$ model of leptons along these lines, originating from $SO(3)\\times U(1)$, which leads to a phenomenologically acceptable pattern of lepton mixing and masses once subleading corrections are taken into account. We also discuss the phenomenological consequences of having a gauged $SO(3)$, leading to massive gauge bos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10292","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":"1809.10292","created_at":"2026-05-17T23:58:30.467387+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.10292v2","created_at":"2026-05-17T23:58:30.467387+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10292","created_at":"2026-05-17T23:58:30.467387+00:00"},{"alias_kind":"pith_short_12","alias_value":"7S762SNQAHA4","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7S762SNQAHA44CXF","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7S762SNQ","created_at":"2026-05-18T12:32:11.075285+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.02770","citing_title":"Trimaximal TM$_1$ mixing with two modular $S_4$ groups","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7S762SNQAHA44CXFO4FJ5ASY5I","json":"https://pith.science/pith/7S762SNQAHA44CXFO4FJ5ASY5I.json","graph_json":"https://pith.science/api/pith-number/7S762SNQAHA44CXFO4FJ5ASY5I/graph.json","events_json":"https://pith.science/api/pith-number/7S762SNQAHA44CXFO4FJ5ASY5I/events.json","paper":"https://pith.science/paper/7S762SNQ"},"agent_actions":{"view_html":"https://pith.science/pith/7S762SNQAHA44CXFO4FJ5ASY5I","download_json":"https://pith.science/pith/7S762SNQAHA44CXFO4FJ5ASY5I.json","view_paper":"https://pith.science/paper/7S762SNQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.10292&json=true","fetch_graph":"https://pith.science/api/pith-number/7S762SNQAHA44CXFO4FJ5ASY5I/graph.json","fetch_events":"https://pith.science/api/pith-number/7S762SNQAHA44CXFO4FJ5ASY5I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7S762SNQAHA44CXFO4FJ5ASY5I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7S762SNQAHA44CXFO4FJ5ASY5I/action/storage_attestation","attest_author":"https://pith.science/pith/7S762SNQAHA44CXFO4FJ5ASY5I/action/author_attestation","sign_citation":"https://pith.science/pith/7S762SNQAHA44CXFO4FJ5ASY5I/action/citation_signature","submit_replication":"https://pith.science/pith/7S762SNQAHA44CXFO4FJ5ASY5I/action/replication_record"}},"created_at":"2026-05-17T23:58:30.467387+00:00","updated_at":"2026-05-17T23:58:30.467387+00:00"}