{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NOCY4THNNEYEDYVHVGJ6EYXUGI","short_pith_number":"pith:NOCY4THN","canonical_record":{"source":{"id":"1505.03798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-05-14T16:57:22Z","cross_cats_sorted":[],"title_canon_sha256":"dc6070a944865beb7e77e1a87481b2f1e0e7511cd50982da43b670efc0744327","abstract_canon_sha256":"a0af7ab447e5cca128006a116a608fb65ed4447bc27f343aa3dfdea3df7b353f"},"schema_version":"1.0"},"canonical_sha256":"6b858e4ced693041e2a7a993e262f432053bf5f5a4114c1e2d90bac59dd80df7","source":{"kind":"arxiv","id":"1505.03798","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03798","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03798v2","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03798","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"pith_short_12","alias_value":"NOCY4THNNEYE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NOCY4THNNEYEDYVH","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NOCY4THN","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NOCY4THNNEYEDYVHVGJ6EYXUGI","target":"record","payload":{"canonical_record":{"source":{"id":"1505.03798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-05-14T16:57:22Z","cross_cats_sorted":[],"title_canon_sha256":"dc6070a944865beb7e77e1a87481b2f1e0e7511cd50982da43b670efc0744327","abstract_canon_sha256":"a0af7ab447e5cca128006a116a608fb65ed4447bc27f343aa3dfdea3df7b353f"},"schema_version":"1.0"},"canonical_sha256":"6b858e4ced693041e2a7a993e262f432053bf5f5a4114c1e2d90bac59dd80df7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:31.656529Z","signature_b64":"ykogk1NFSVKSjUxSj9oRfwhwINNLIzJlkBtlumBV3363Kc6cdJPSEM3dJGjKsrj+H2rRdbDYOYz8fjZvPeklAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b858e4ced693041e2a7a993e262f432053bf5f5a4114c1e2d90bac59dd80df7","last_reissued_at":"2026-05-18T01:25:31.655855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:31.655855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.03798","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FqPTl+ishqBvan8FeWkYHengWCvTl4uKlt9qPwtEaQKfA/BuZpsjAhnSu8Wd3R0FB9oQ3YH8oa3QQ9ajmyXVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T17:24:00.398414Z"},"content_sha256":"5db5783238271409dca404f0600c52a3c816f78a41a9e862baa60412367cb01c","schema_version":"1.0","event_id":"sha256:5db5783238271409dca404f0600c52a3c816f78a41a9e862baa60412367cb01c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NOCY4THNNEYEDYVHVGJ6EYXUGI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lepton and Quark Mixing Patterns from Finite Flavor Symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Chang-Yuan Yao, Gui-Jun Ding","submitted_at":"2015-05-14T16:57:22Z","abstract_excerpt":"We perform a systematical and analytical study of lepton mixing which can be derived from the subgroups of $SU(3)$ under the assumption that neutrinos are Dirac particles. We find that type D groups can predict lepton mixing patterns compatible with the experimental data at $3\\sigma$ level. The lepton mixing matrix turns out to be of the trimaximal form, and the Dirac CP violating phase is trivial. Moreover, we extend the flavor symmetry to the quark sector. The Cabibbo mixing between the first two generations of quarks can be generated by type D groups. Since all the finite subgroups of $U(3)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03798","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PgCkVdPZSDFp4pFVH2SNx/HfxvcnNF8d404ZDiIbO752Yx5qJnaRHoDLhLIIDa1rak5K45QosOgiU6QtJBnVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T17:24:00.398763Z"},"content_sha256":"b48662769d5dd2da7a9bee4cda8131065c87df98d50d891bafd666bb139ca44c","schema_version":"1.0","event_id":"sha256:b48662769d5dd2da7a9bee4cda8131065c87df98d50d891bafd666bb139ca44c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NOCY4THNNEYEDYVHVGJ6EYXUGI/bundle.json","state_url":"https://pith.science/pith/NOCY4THNNEYEDYVHVGJ6EYXUGI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NOCY4THNNEYEDYVHVGJ6EYXUGI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-28T17:24:00Z","links":{"resolver":"https://pith.science/pith/NOCY4THNNEYEDYVHVGJ6EYXUGI","bundle":"https://pith.science/pith/NOCY4THNNEYEDYVHVGJ6EYXUGI/bundle.json","state":"https://pith.science/pith/NOCY4THNNEYEDYVHVGJ6EYXUGI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NOCY4THNNEYEDYVHVGJ6EYXUGI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NOCY4THNNEYEDYVHVGJ6EYXUGI","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":"a0af7ab447e5cca128006a116a608fb65ed4447bc27f343aa3dfdea3df7b353f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-05-14T16:57:22Z","title_canon_sha256":"dc6070a944865beb7e77e1a87481b2f1e0e7511cd50982da43b670efc0744327"},"schema_version":"1.0","source":{"id":"1505.03798","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03798","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03798v2","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03798","created_at":"2026-05-18T01:25:31Z"},{"alias_kind":"pith_short_12","alias_value":"NOCY4THNNEYE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NOCY4THNNEYEDYVH","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NOCY4THN","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:b48662769d5dd2da7a9bee4cda8131065c87df98d50d891bafd666bb139ca44c","target":"graph","created_at":"2026-05-18T01:25:31Z","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 perform a systematical and analytical study of lepton mixing which can be derived from the subgroups of $SU(3)$ under the assumption that neutrinos are Dirac particles. We find that type D groups can predict lepton mixing patterns compatible with the experimental data at $3\\sigma$ level. The lepton mixing matrix turns out to be of the trimaximal form, and the Dirac CP violating phase is trivial. Moreover, we extend the flavor symmetry to the quark sector. The Cabibbo mixing between the first two generations of quarks can be generated by type D groups. Since all the finite subgroups of $U(3)","authors_text":"Chang-Yuan Yao, Gui-Jun Ding","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-05-14T16:57:22Z","title":"Lepton and Quark Mixing Patterns from Finite Flavor Symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03798","kind":"arxiv","version":2},"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":"sha256:5db5783238271409dca404f0600c52a3c816f78a41a9e862baa60412367cb01c","target":"record","created_at":"2026-05-18T01:25:31Z","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":"a0af7ab447e5cca128006a116a608fb65ed4447bc27f343aa3dfdea3df7b353f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-05-14T16:57:22Z","title_canon_sha256":"dc6070a944865beb7e77e1a87481b2f1e0e7511cd50982da43b670efc0744327"},"schema_version":"1.0","source":{"id":"1505.03798","kind":"arxiv","version":2}},"canonical_sha256":"6b858e4ced693041e2a7a993e262f432053bf5f5a4114c1e2d90bac59dd80df7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b858e4ced693041e2a7a993e262f432053bf5f5a4114c1e2d90bac59dd80df7","first_computed_at":"2026-05-18T01:25:31.655855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:31.655855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ykogk1NFSVKSjUxSj9oRfwhwINNLIzJlkBtlumBV3363Kc6cdJPSEM3dJGjKsrj+H2rRdbDYOYz8fjZvPeklAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:31.656529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03798","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5db5783238271409dca404f0600c52a3c816f78a41a9e862baa60412367cb01c","sha256:b48662769d5dd2da7a9bee4cda8131065c87df98d50d891bafd666bb139ca44c"],"state_sha256":"fe48f6d893fcd5d2365cdb98b76d0e453f2817f7bba2bb587bbde1935617570d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"77QWnqSX90c+kAsFIr9WW5oZe/HRAUIiQGyrANRp5EQpWbfSQ2EF8WxpHb/zE0lB4rY7CUeLrRJnMKSQomLtDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T17:24:00.400839Z","bundle_sha256":"fe92ca1279936d080a564dd55708e7a6538d3fce0ca34dfa30c11af7aec0638b"}}