{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HUCH2L6TUA3WZE6IVFQLNVXI7D","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f6712a9706c98b38adfa784e956541af4fdb4007e0aca504f279256844e53315","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-01-12T18:18:41Z","title_canon_sha256":"c7cfd8b16df049e612fe0da67c9a8be54f685826c598bfa24c462ff297346e1b"},"schema_version":"1.0","source":{"id":"1101.2417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2417","created_at":"2026-05-18T02:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2417v1","created_at":"2026-05-18T02:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2417","created_at":"2026-05-18T02:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"HUCH2L6TUA3W","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HUCH2L6TUA3WZE6I","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HUCH2L6T","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:51a5461ba69b548b0284171e649b9577ab996da41d1a2a2a1ccc6ee6eb85999e","target":"graph","created_at":"2026-05-18T02:22:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Non-Abelian discrete family symmetries play a pivotal role in the formulation of models with tri-bimaximal lepton mixing. We discuss how to obtain symmetries such as A4, semidirect product of Z7 and Z3, and Delta(27) from an underlying SU(3) gauge symmetry. Higher irreducible representations are required to achieve the spontaneous breaking of the continuous group. We present methods of identifying the required vacuum alignments and discuss in detail the symmetry breaking potentials.","authors_text":"Christoph Luhn","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-01-12T18:18:41Z","title":"Spontaneous breaking of SU(3) to finite family symmetries: a pedestrian's approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2417","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4beb3505282ada3596a3cf08362318d0af202b5f43955deac29a7dc094c72ebb","target":"record","created_at":"2026-05-18T02:22:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f6712a9706c98b38adfa784e956541af4fdb4007e0aca504f279256844e53315","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-01-12T18:18:41Z","title_canon_sha256":"c7cfd8b16df049e612fe0da67c9a8be54f685826c598bfa24c462ff297346e1b"},"schema_version":"1.0","source":{"id":"1101.2417","kind":"arxiv","version":1}},"canonical_sha256":"3d047d2fd3a0376c93c8a960b6d6e8f8c599647554fa5f7de916ac14f9ef00a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d047d2fd3a0376c93c8a960b6d6e8f8c599647554fa5f7de916ac14f9ef00a5","first_computed_at":"2026-05-18T02:22:58.147616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:58.147616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ABMISJ9hVVp9MMVuQ+B4W4Tob1a7TfHZoPeYAbp1XGcUVxq1OrKTTIXht7hJvoOxlBbTTB5pbAvz8Wd3SLbFCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:58.148080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4beb3505282ada3596a3cf08362318d0af202b5f43955deac29a7dc094c72ebb","sha256:51a5461ba69b548b0284171e649b9577ab996da41d1a2a2a1ccc6ee6eb85999e"],"state_sha256":"02b1d284c220d55631bec0b7b2377728124565de4c1ffd386d95e280230744d3"}