{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6PQK7G6TFZVIUIKCR4SMHILA2G","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":"3300e34ac3e6f9cc0f5561f74d5fae498d883460c65f6b3acbfe5a15d8a801df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-12-06T16:37:40Z","title_canon_sha256":"90e26e7fad020313b5694ee1827584519c6604d093562ff292e63fa5eae8b10d"},"schema_version":"1.0","source":{"id":"1112.1340","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1340","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1340v1","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1340","created_at":"2026-05-18T01:59:16Z"},{"alias_kind":"pith_short_12","alias_value":"6PQK7G6TFZVI","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6PQK7G6TFZVIUIKC","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6PQK7G6T","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:0c84e181918ecd0ee6924f009d793761eb9cf8c979bbb5418291bf06be122a7c","target":"graph","created_at":"2026-05-18T01:59:16Z","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":"We study lepton mixing patterns which are derived from finite modular groups Gamma_N, requiring subgroups G_nu and G_e to be preserved in the neutrino and charged lepton sectors, respectively. We show that only six groups Gamma_N with N=3,4,5,7,8,16 are relevant. A comprehensive analysis is presented for G_e arbitrary and G_nu=Z2 x Z2, as demanded if neutrinos are Majorana particles. We discuss interesting patterns arising from both groups G_e and G_nu being arbitrary. Several of the most promising patterns are specific deviations from tri-bimaximal mixing, all predicting theta_13 non-zero as ","authors_text":"Claudia Hagedorn, Ferruccio Feruglio, Reinier de Adelhart Toorop","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-12-06T16:37:40Z","title":"Finite Modular Groups and Lepton Mixing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1340","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":"sha256:6fd6d33bb248032de866448b95bf7612365462494e74e12f811dd6d36bb3846e","target":"record","created_at":"2026-05-18T01:59:16Z","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":"3300e34ac3e6f9cc0f5561f74d5fae498d883460c65f6b3acbfe5a15d8a801df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2011-12-06T16:37:40Z","title_canon_sha256":"90e26e7fad020313b5694ee1827584519c6604d093562ff292e63fa5eae8b10d"},"schema_version":"1.0","source":{"id":"1112.1340","kind":"arxiv","version":1}},"canonical_sha256":"f3e0af9bd32e6a8a21428f24c3a160d19c5927086aaebc52132ba85c0f343f2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3e0af9bd32e6a8a21428f24c3a160d19c5927086aaebc52132ba85c0f343f2d","first_computed_at":"2026-05-18T01:59:16.334599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:16.334599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iI33brMs1OKPs8uGgcXs1USwuoxK0PjEzARFJBK66MLQA78Kt1KHDRnUwVLBENbW2YUoPkLQn8UHfCm3O35nBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:16.335416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1340","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fd6d33bb248032de866448b95bf7612365462494e74e12f811dd6d36bb3846e","sha256:0c84e181918ecd0ee6924f009d793761eb9cf8c979bbb5418291bf06be122a7c"],"state_sha256":"54c3ddcbace3e5366076ca709f2f7a0bffb30e860b5ee406e79585b91871bac7"}