{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DNILRFJWYP26FBXSBYOGVLYIV4","short_pith_number":"pith:DNILRFJW","canonical_record":{"source":{"id":"1907.11714","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-07-26T10:11:01Z","cross_cats_sorted":[],"title_canon_sha256":"b6b56fc0bb5c89ec314c12176529f763ce2953767551e0377c1b2c3810cd4892","abstract_canon_sha256":"11a9b165ceba963ef1c64fa32a733559374f2292e053486e0b6cb0bd815375d9"},"schema_version":"1.0"},"canonical_sha256":"1b50b89536c3f5e286f20e1c6aaf08af017a8f98a0ec6fb74ce733577f201e9c","source":{"kind":"arxiv","id":"1907.11714","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11714","created_at":"2026-07-05T00:08:35Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11714v1","created_at":"2026-07-05T00:08:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11714","created_at":"2026-07-05T00:08:35Z"},{"alias_kind":"pith_short_12","alias_value":"DNILRFJWYP26","created_at":"2026-07-05T00:08:35Z"},{"alias_kind":"pith_short_16","alias_value":"DNILRFJWYP26FBXS","created_at":"2026-07-05T00:08:35Z"},{"alias_kind":"pith_short_8","alias_value":"DNILRFJW","created_at":"2026-07-05T00:08:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DNILRFJWYP26FBXSBYOGVLYIV4","target":"record","payload":{"canonical_record":{"source":{"id":"1907.11714","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-07-26T10:11:01Z","cross_cats_sorted":[],"title_canon_sha256":"b6b56fc0bb5c89ec314c12176529f763ce2953767551e0377c1b2c3810cd4892","abstract_canon_sha256":"11a9b165ceba963ef1c64fa32a733559374f2292e053486e0b6cb0bd815375d9"},"schema_version":"1.0"},"canonical_sha256":"1b50b89536c3f5e286f20e1c6aaf08af017a8f98a0ec6fb74ce733577f201e9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:08:35.794245Z","signature_b64":"jfH95TmxituxYV/0Cus0CsgAMSuqLOkxyQkU03Hud2OyDJFo95oL66SEYz5lFZTRRGwWDJ6dPcdT9YG0ys4wCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b50b89536c3f5e286f20e1c6aaf08af017a8f98a0ec6fb74ce733577f201e9c","last_reissued_at":"2026-07-05T00:08:35.793893Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:08:35.793893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.11714","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:08:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dnh4EkRtiddO5d7HBVCr5ldoXg3lMw+d5Km9hqqXYI8bkhvukm/9amN7K6TnHm82diqBFVGOclIv+nzfipJWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:25:57.588407Z"},"content_sha256":"92d2a43d791e49955a80e1a0430a4f88ff589f1c449d140670623b8e46b2d410","schema_version":"1.0","event_id":"sha256:92d2a43d791e49955a80e1a0430a4f88ff589f1c449d140670623b8e46b2d410"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DNILRFJWYP26FBXSBYOGVLYIV4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular $A_4$ Symmetry Models of Neutrinos and Charged Leptons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Gui-Jun Ding, Stephen F. King, Xiang-Gan Liu","submitted_at":"2019-07-26T10:11:01Z","abstract_excerpt":"We present a comprehensive analysis of neutrino mass and lepton mixing in theories with $A_4$ modular symmetry, where the only flavon field is the single modulus field $\\tau$, and all masses and Yukawa couplings are modular forms. Similar to previous analyses, we discuss all the simplest neutrino sectors arising from both the Weinberg operator and the type I seesaw mechanism, with lepton doublets and right-handed neutrinos assumed to be triplets of $A_4$. Unlike previous analyses, we allow right-handed charged leptons to transform as all combinations of $\\mathbf{1}$, $\\mathbf{1}'$ and $\\mathbf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11714","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.11714/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:08:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WaU8fhLSBmE5jMka9kjTYCXa+qCw6itGpQuHYogPW65yEh/99YcU4fqA03kLgf5oV7IphuRSiSPUz+yfYtn6Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:25:57.588783Z"},"content_sha256":"b8e8e73ba6351e399252d5650c6c13fe00b5b5a4317ee6c0df1a10df7190cc47","schema_version":"1.0","event_id":"sha256:b8e8e73ba6351e399252d5650c6c13fe00b5b5a4317ee6c0df1a10df7190cc47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNILRFJWYP26FBXSBYOGVLYIV4/bundle.json","state_url":"https://pith.science/pith/DNILRFJWYP26FBXSBYOGVLYIV4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNILRFJWYP26FBXSBYOGVLYIV4/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":"2026-07-07T08:25:57Z","links":{"resolver":"https://pith.science/pith/DNILRFJWYP26FBXSBYOGVLYIV4","bundle":"https://pith.science/pith/DNILRFJWYP26FBXSBYOGVLYIV4/bundle.json","state":"https://pith.science/pith/DNILRFJWYP26FBXSBYOGVLYIV4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNILRFJWYP26FBXSBYOGVLYIV4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DNILRFJWYP26FBXSBYOGVLYIV4","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":"11a9b165ceba963ef1c64fa32a733559374f2292e053486e0b6cb0bd815375d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-07-26T10:11:01Z","title_canon_sha256":"b6b56fc0bb5c89ec314c12176529f763ce2953767551e0377c1b2c3810cd4892"},"schema_version":"1.0","source":{"id":"1907.11714","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11714","created_at":"2026-07-05T00:08:35Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11714v1","created_at":"2026-07-05T00:08:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11714","created_at":"2026-07-05T00:08:35Z"},{"alias_kind":"pith_short_12","alias_value":"DNILRFJWYP26","created_at":"2026-07-05T00:08:35Z"},{"alias_kind":"pith_short_16","alias_value":"DNILRFJWYP26FBXS","created_at":"2026-07-05T00:08:35Z"},{"alias_kind":"pith_short_8","alias_value":"DNILRFJW","created_at":"2026-07-05T00:08:35Z"}],"graph_snapshots":[{"event_id":"sha256:b8e8e73ba6351e399252d5650c6c13fe00b5b5a4317ee6c0df1a10df7190cc47","target":"graph","created_at":"2026-07-05T00:08:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1907.11714/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a comprehensive analysis of neutrino mass and lepton mixing in theories with $A_4$ modular symmetry, where the only flavon field is the single modulus field $\\tau$, and all masses and Yukawa couplings are modular forms. Similar to previous analyses, we discuss all the simplest neutrino sectors arising from both the Weinberg operator and the type I seesaw mechanism, with lepton doublets and right-handed neutrinos assumed to be triplets of $A_4$. Unlike previous analyses, we allow right-handed charged leptons to transform as all combinations of $\\mathbf{1}$, $\\mathbf{1}'$ and $\\mathbf","authors_text":"Gui-Jun Ding, Stephen F. King, Xiang-Gan Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-07-26T10:11:01Z","title":"Modular $A_4$ Symmetry Models of Neutrinos and Charged Leptons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11714","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":"sha256:92d2a43d791e49955a80e1a0430a4f88ff589f1c449d140670623b8e46b2d410","target":"record","created_at":"2026-07-05T00:08:35Z","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":"11a9b165ceba963ef1c64fa32a733559374f2292e053486e0b6cb0bd815375d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2019-07-26T10:11:01Z","title_canon_sha256":"b6b56fc0bb5c89ec314c12176529f763ce2953767551e0377c1b2c3810cd4892"},"schema_version":"1.0","source":{"id":"1907.11714","kind":"arxiv","version":1}},"canonical_sha256":"1b50b89536c3f5e286f20e1c6aaf08af017a8f98a0ec6fb74ce733577f201e9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b50b89536c3f5e286f20e1c6aaf08af017a8f98a0ec6fb74ce733577f201e9c","first_computed_at":"2026-07-05T00:08:35.793893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:08:35.793893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jfH95TmxituxYV/0Cus0CsgAMSuqLOkxyQkU03Hud2OyDJFo95oL66SEYz5lFZTRRGwWDJ6dPcdT9YG0ys4wCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:08:35.794245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.11714","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92d2a43d791e49955a80e1a0430a4f88ff589f1c449d140670623b8e46b2d410","sha256:b8e8e73ba6351e399252d5650c6c13fe00b5b5a4317ee6c0df1a10df7190cc47"],"state_sha256":"972e32e423fed1e22b4e66303792f7f80f161e231ece6951ac55dfa95f683b35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OmKGj35ALmdt/CZbeM1Ad18EvOrnXyU0QbCm6RIrAfegvcq7GHxO+JlX6kZd6InC2o0UNLXk9tqa8WNpn7TXCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T08:25:57.590689Z","bundle_sha256":"9285fcfa10a7f55377d7e3d6b2a150dd3ff2a95512c109c891964c98c5e2a6d1"}}