{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:MJXDJQCS3GWJRK57OEQ7AMB2XT","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":"7d4a9be18abe93b1f1ab715842e69b4fd4e43dd237221c2faa57dd2b25358c48","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2020-06-18T17:52:15Z","title_canon_sha256":"14b290a2a82ef2f31f32cd58df8fe4b735e71063c9df4c5a91d097f580b416c4"},"schema_version":"1.0","source":{"id":"2006.10722","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.10722","created_at":"2026-07-05T02:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"2006.10722v2","created_at":"2026-07-05T02:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.10722","created_at":"2026-07-05T02:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"MJXDJQCS3GWJ","created_at":"2026-07-05T02:27:21Z"},{"alias_kind":"pith_short_16","alias_value":"MJXDJQCS3GWJRK57","created_at":"2026-07-05T02:27:21Z"},{"alias_kind":"pith_short_8","alias_value":"MJXDJQCS","created_at":"2026-07-05T02:27:21Z"}],"graph_snapshots":[{"event_id":"sha256:8d82fa8747ae9af34bb686d78e43451a59f924df8fbb2a6fd5ee33ecf0e30be5","target":"graph","created_at":"2026-07-05T02:27:21Z","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/2006.10722/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We perform a comprehensive analysis of the homogeneous finite modular group $\\Gamma'_4\\equiv S'_4$ which is the double covering of $S_4$ group. The weight 1 modular forms of level 4 are constructed in terms of Dedekind eta function, and they transform as a triplet $\\mathbf{\\hat{3}'}$ of $S'_4$. The integral weight modular forms until weight 6 are built from the tensor products of weight 1 modular forms. We perform a systematical classification of $S'_4$ modular models for lepton masses and mixing with/without generalized CP, where the left-handed leptons are assigned to triplet of $S'_4$ and r","authors_text":"Chang-Yuan Yao, Gui-Jun Ding, Xiang-Gan Liu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2020-06-18T17:52:15Z","title":"Modular Invariant Quark and Lepton Models in Double Covering of $S_4$ Modular Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.10722","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":"sha256:44f1fe8feea3cc3b5476167797ef542132ded57bf72fcf167ad87ba8d33a68ae","target":"record","created_at":"2026-07-05T02:27:21Z","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":"7d4a9be18abe93b1f1ab715842e69b4fd4e43dd237221c2faa57dd2b25358c48","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2020-06-18T17:52:15Z","title_canon_sha256":"14b290a2a82ef2f31f32cd58df8fe4b735e71063c9df4c5a91d097f580b416c4"},"schema_version":"1.0","source":{"id":"2006.10722","kind":"arxiv","version":2}},"canonical_sha256":"626e34c052d9ac98abbf7121f0303abcf49306ecba15b987c115ebb3fccca956","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"626e34c052d9ac98abbf7121f0303abcf49306ecba15b987c115ebb3fccca956","first_computed_at":"2026-07-05T02:27:21.507405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:27:21.507405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l2apBuE6estvPNEVqKL10rvYGPUAbgut+cyGCZtfdQkZ5X4sZmXvTG3VebMZi7vj9/q5qCE81baXkTNoFpBqDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:27:21.507884Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.10722","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44f1fe8feea3cc3b5476167797ef542132ded57bf72fcf167ad87ba8d33a68ae","sha256:8d82fa8747ae9af34bb686d78e43451a59f924df8fbb2a6fd5ee33ecf0e30be5"],"state_sha256":"576007fb021e709edb33af97f2b89f16807a60f81102a70317c15efea81eab05"}