{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JAEUNI4C4VCM33MBATL7WDLANR","short_pith_number":"pith:JAEUNI4C","canonical_record":{"source":{"id":"1507.00338","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-07-01T20:00:18Z","cross_cats_sorted":[],"title_canon_sha256":"506d3ecc2a29dbbc73446dcb65885bd854314a6c1144c828002d6267c2688e35","abstract_canon_sha256":"3189a61f5e23a5e8ecba3a73a5247d41d1c55a7e0c1af5d0d4724d57be72e0f6"},"schema_version":"1.0"},"canonical_sha256":"480946a382e544cded8104d7fb0d606c7b6129207404f3673c49ffc70fb99df6","source":{"kind":"arxiv","id":"1507.00338","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00338","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00338v2","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00338","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"pith_short_12","alias_value":"JAEUNI4C4VCM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JAEUNI4C4VCM33MB","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JAEUNI4C","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JAEUNI4C4VCM33MBATL7WDLANR","target":"record","payload":{"canonical_record":{"source":{"id":"1507.00338","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-07-01T20:00:18Z","cross_cats_sorted":[],"title_canon_sha256":"506d3ecc2a29dbbc73446dcb65885bd854314a6c1144c828002d6267c2688e35","abstract_canon_sha256":"3189a61f5e23a5e8ecba3a73a5247d41d1c55a7e0c1af5d0d4724d57be72e0f6"},"schema_version":"1.0"},"canonical_sha256":"480946a382e544cded8104d7fb0d606c7b6129207404f3673c49ffc70fb99df6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:59.475249Z","signature_b64":"DBpfM0tQIIN3qAwytFBD2y5SHzA47Tv260aX8SNE4tbYAW+vV1iuawUCMELs2fwFFnb7HTku5mEuYybnsDchBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"480946a382e544cded8104d7fb0d606c7b6129207404f3673c49ffc70fb99df6","last_reissued_at":"2026-05-18T01:35:59.474609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:59.474609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.00338","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":"2026-05-18T01:35:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8xirzPMF+S4Ri/UUX5rXUgtPQT6/OskGPoH9fK5mCkB3kWpf5Nss1aeQ7mP8RKR12pF+iknnW9/omkY27BQlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:23:03.559617Z"},"content_sha256":"e93047b5147e2ab876c9ded0d144c0be044561b72eff5545050801cf61a932b1","schema_version":"1.0","event_id":"sha256:e93047b5147e2ab876c9ded0d144c0be044561b72eff5545050801cf61a932b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JAEUNI4C4VCM33MBATL7WDLANR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\Delta(27)$ family symmetry and neutrino mixing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Ivo de Medeiros Varzielas","submitted_at":"2015-07-01T20:00:18Z","abstract_excerpt":"The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal. This structure may be related to the existence of a discrete non-Abelian family symmetry.\n  In this paper the family symmetry is the non-Abelian discrete group $\\Delta(27)$, a subgroup of $SU(3)$ with triplet and anti-triplet representations. Different frameworks are constructed in which the mixing follows from combining fermion mass terms with the vacuum structure enforced by the discrete symmetry. Mass terms for the fermions originate from familon "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00338","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":"2026-05-18T01:35:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xVyjsfl24ug74QpZyQMCqC7a1+kkxyL++QkbWu4k8Aex7Vetyk7+atGuTF5XC7k5dsodHD8Sd87YzEumNz/pBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:23:03.559976Z"},"content_sha256":"4b047a9aa461bd09b79eeae4d292076cde6c873c0c2006cc75a848acb3153a93","schema_version":"1.0","event_id":"sha256:4b047a9aa461bd09b79eeae4d292076cde6c873c0c2006cc75a848acb3153a93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JAEUNI4C4VCM33MBATL7WDLANR/bundle.json","state_url":"https://pith.science/pith/JAEUNI4C4VCM33MBATL7WDLANR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JAEUNI4C4VCM33MBATL7WDLANR/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":"2026-05-31T21:23:03Z","links":{"resolver":"https://pith.science/pith/JAEUNI4C4VCM33MBATL7WDLANR","bundle":"https://pith.science/pith/JAEUNI4C4VCM33MBATL7WDLANR/bundle.json","state":"https://pith.science/pith/JAEUNI4C4VCM33MBATL7WDLANR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JAEUNI4C4VCM33MBATL7WDLANR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JAEUNI4C4VCM33MBATL7WDLANR","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":"3189a61f5e23a5e8ecba3a73a5247d41d1c55a7e0c1af5d0d4724d57be72e0f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-07-01T20:00:18Z","title_canon_sha256":"506d3ecc2a29dbbc73446dcb65885bd854314a6c1144c828002d6267c2688e35"},"schema_version":"1.0","source":{"id":"1507.00338","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00338","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00338v2","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00338","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"pith_short_12","alias_value":"JAEUNI4C4VCM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JAEUNI4C4VCM33MB","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JAEUNI4C","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:4b047a9aa461bd09b79eeae4d292076cde6c873c0c2006cc75a848acb3153a93","target":"graph","created_at":"2026-05-18T01:35:59Z","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":"The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal. This structure may be related to the existence of a discrete non-Abelian family symmetry.\n  In this paper the family symmetry is the non-Abelian discrete group $\\Delta(27)$, a subgroup of $SU(3)$ with triplet and anti-triplet representations. Different frameworks are constructed in which the mixing follows from combining fermion mass terms with the vacuum structure enforced by the discrete symmetry. Mass terms for the fermions originate from familon ","authors_text":"Ivo de Medeiros Varzielas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-07-01T20:00:18Z","title":"$\\Delta(27)$ family symmetry and neutrino mixing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00338","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:e93047b5147e2ab876c9ded0d144c0be044561b72eff5545050801cf61a932b1","target":"record","created_at":"2026-05-18T01:35:59Z","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":"3189a61f5e23a5e8ecba3a73a5247d41d1c55a7e0c1af5d0d4724d57be72e0f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-07-01T20:00:18Z","title_canon_sha256":"506d3ecc2a29dbbc73446dcb65885bd854314a6c1144c828002d6267c2688e35"},"schema_version":"1.0","source":{"id":"1507.00338","kind":"arxiv","version":2}},"canonical_sha256":"480946a382e544cded8104d7fb0d606c7b6129207404f3673c49ffc70fb99df6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"480946a382e544cded8104d7fb0d606c7b6129207404f3673c49ffc70fb99df6","first_computed_at":"2026-05-18T01:35:59.474609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:59.474609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DBpfM0tQIIN3qAwytFBD2y5SHzA47Tv260aX8SNE4tbYAW+vV1iuawUCMELs2fwFFnb7HTku5mEuYybnsDchBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:59.475249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00338","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e93047b5147e2ab876c9ded0d144c0be044561b72eff5545050801cf61a932b1","sha256:4b047a9aa461bd09b79eeae4d292076cde6c873c0c2006cc75a848acb3153a93"],"state_sha256":"a14c49a3392547ea0ffbe0b2361aba363ce7dd52a28da155ad0d71cd61f64f33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qJCRf/LsiKxIdco00d/L1ugj85NN3ZD/eeb93sMjcFF0TMAAvx+AiIhxAYXQCoesKcJKcF66Bq4QU/5mkf4vBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:23:03.561941Z","bundle_sha256":"8be7cb81c47f1ec3592ef63f3597b05811c47e59c3f2c4c1b59181890255d016"}}