{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LRE5YTC737LIQXAFQ6DUAVEXIU","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":"9328f483d703234680c965a7762db2e026cd11c6e5061d385c48095cc24d8b51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-06-18T14:06:06Z","title_canon_sha256":"b2240226da9d6a1870bddcac5a828354dca09c131df2473fdaba538d77a7243f"},"schema_version":"1.0","source":{"id":"2306.10569","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.10569","created_at":"2026-07-05T08:25:48Z"},{"alias_kind":"arxiv_version","alias_value":"2306.10569v3","created_at":"2026-07-05T08:25:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.10569","created_at":"2026-07-05T08:25:48Z"},{"alias_kind":"pith_short_12","alias_value":"LRE5YTC737LI","created_at":"2026-07-05T08:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"LRE5YTC737LIQXAF","created_at":"2026-07-05T08:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"LRE5YTC7","created_at":"2026-07-05T08:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:8ec9026421d85d62e1b06241c1cb1db87e82a4248846a296b4ebcad751955dea","target":"graph","created_at":"2026-07-05T08:25:48Z","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/2306.10569/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Flavored modular differential equations sometimes arise from null states or their descendants in a chiral algebra with continuous flavor symmetry. In this paper we focus on Kac-Moody algebras $\\widehat{\\mathfrak{g}}_k$ that contain a level-four null state $|\\mathcal{N}_T\\rangle$ which implements the nilpotency of the Sugawara stress tensor. We study the properties of the corresponding flavored modular differential equations, and show that the equations exhibit almost covariance under modular $S$-transformation, connecting null states and their descendants at different levels. The modular prope","authors_text":"Yiwen Pan, Yufan Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-06-18T14:06:06Z","title":"Flavored modular differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.10569","kind":"arxiv","version":3},"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":"sha256:0650ee36774edc2b865be4e1f28b66cb592e734693845ff5d22bd13b935cc6b7","target":"record","created_at":"2026-07-05T08:25:48Z","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":"9328f483d703234680c965a7762db2e026cd11c6e5061d385c48095cc24d8b51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-06-18T14:06:06Z","title_canon_sha256":"b2240226da9d6a1870bddcac5a828354dca09c131df2473fdaba538d77a7243f"},"schema_version":"1.0","source":{"id":"2306.10569","kind":"arxiv","version":3}},"canonical_sha256":"5c49dc4c5fdfd6885c05878740549745320dd2c8036d4f0dda52702f3c80ed5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c49dc4c5fdfd6885c05878740549745320dd2c8036d4f0dda52702f3c80ed5d","first_computed_at":"2026-07-05T08:25:48.742091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:25:48.742091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c9EbCYukrseD/3QpCZSI+VbELnm5VP2gwHOh8Vl/Y9KxLiGQVWFUA8Lcdf9H25ePHvnjRoT0M4K4/3OftR0yCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:25:48.742634Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.10569","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0650ee36774edc2b865be4e1f28b66cb592e734693845ff5d22bd13b935cc6b7","sha256:8ec9026421d85d62e1b06241c1cb1db87e82a4248846a296b4ebcad751955dea"],"state_sha256":"30a8bf763742adc81e6ab429699c7b34790b5e962c18b7320774d27a9e3cd7f2"}