{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5QQLQI6IFQ577G5NP3G7V6343O","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":"22ba5a381bee7ac0939fd7dbc6fd4517b145e4e671deefa1f6576545b8834b1b","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-12-06T17:01:28Z","title_canon_sha256":"dd12de14d0fbffc39d63b97ecb6f22cc3df0ab8912e7bc3938baf36ce8722b0d"},"schema_version":"1.0","source":{"id":"2212.03136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.03136","created_at":"2026-07-05T06:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"2212.03136v1","created_at":"2026-07-05T06:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.03136","created_at":"2026-07-05T06:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"5QQLQI6IFQ57","created_at":"2026-07-05T06:37:11Z"},{"alias_kind":"pith_short_16","alias_value":"5QQLQI6IFQ577G5N","created_at":"2026-07-05T06:37:11Z"},{"alias_kind":"pith_short_8","alias_value":"5QQLQI6I","created_at":"2026-07-05T06:37:11Z"}],"graph_snapshots":[{"event_id":"sha256:be40d8f49457399458aacbcacf98aceba47b33f5cc58cf7f529d0fc1e2ec87dd","target":"graph","created_at":"2026-07-05T06:37:11Z","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/2212.03136/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the admissible vector-valued modular forms having three independent characters and vanishing Wronskian index and determine which ones correspond to genuine 2d conformal field theories. This is done by finding bilinear coset-type relations that pair them into meromorphic characters with central charges 8, 16, 24, 32 and 40. Such pairings allow us to identify some characters with definite CFTs and rule out others. As a key result we classify all unitary three-character CFT with vanishing Wronskian index, excluding $c=8,16$. The complete list has two infinite affine series $B_{r,1}","authors_text":"Arpit Das, Chethan N. Gowdigere, Sunil Mukhi","cross_cats":["math-ph","math.MP","math.QA","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-12-06T17:01:28Z","title":"Meromorphic Cosets and the Classification of Three-Character CFT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.03136","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":"sha256:362657a107764bbc397d060408748ec425f2ca41fe861076b6f1e5ac282f948a","target":"record","created_at":"2026-07-05T06:37:11Z","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":"22ba5a381bee7ac0939fd7dbc6fd4517b145e4e671deefa1f6576545b8834b1b","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-12-06T17:01:28Z","title_canon_sha256":"dd12de14d0fbffc39d63b97ecb6f22cc3df0ab8912e7bc3938baf36ce8722b0d"},"schema_version":"1.0","source":{"id":"2212.03136","kind":"arxiv","version":1}},"canonical_sha256":"ec20b823c82c3bff9bad7ecdfafb7cdba749839d37dbfacb84cdd500eb0f9165","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec20b823c82c3bff9bad7ecdfafb7cdba749839d37dbfacb84cdd500eb0f9165","first_computed_at":"2026-07-05T06:37:11.739288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:37:11.739288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F3eb5lkGRgNopQ0WTn8T3cGaxC/8L4zaWuE7kIjSTct4wo42QZxRkvj3A0I7z5MxoJ1GYNv5+KlvXCDA+VcsCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:37:11.739676Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.03136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:362657a107764bbc397d060408748ec425f2ca41fe861076b6f1e5ac282f948a","sha256:be40d8f49457399458aacbcacf98aceba47b33f5cc58cf7f529d0fc1e2ec87dd"],"state_sha256":"e93cb836375596d71bf2be104eb7104e1f304f8aa275f10e17f251b40763c797"}