{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:E2LHLTI565XDLYWGCSMQUMSGFT","short_pith_number":"pith:E2LHLTI5","canonical_record":{"source":{"id":"2304.09681","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2023-04-19T14:19:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"05a74056c5116f933ebd9ae0d82c9bc03d1ff11c01733ec532afbf4e70bba3e5","abstract_canon_sha256":"3b39d0655718b2f466e05cfaac95f7ac0592531951fe9c3dd2016c21313c27be"},"schema_version":"1.0"},"canonical_sha256":"269675cd1df76e35e2c614990a32462cdf857ad68c513e67550b6b2ad56c5a4c","source":{"kind":"arxiv","id":"2304.09681","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.09681","created_at":"2026-07-05T06:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"2304.09681v2","created_at":"2026-07-05T06:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.09681","created_at":"2026-07-05T06:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"E2LHLTI565XD","created_at":"2026-07-05T06:35:50Z"},{"alias_kind":"pith_short_16","alias_value":"E2LHLTI565XDLYWG","created_at":"2026-07-05T06:35:50Z"},{"alias_kind":"pith_short_8","alias_value":"E2LHLTI5","created_at":"2026-07-05T06:35:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:E2LHLTI565XDLYWGCSMQUMSGFT","target":"record","payload":{"canonical_record":{"source":{"id":"2304.09681","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2023-04-19T14:19:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"05a74056c5116f933ebd9ae0d82c9bc03d1ff11c01733ec532afbf4e70bba3e5","abstract_canon_sha256":"3b39d0655718b2f466e05cfaac95f7ac0592531951fe9c3dd2016c21313c27be"},"schema_version":"1.0"},"canonical_sha256":"269675cd1df76e35e2c614990a32462cdf857ad68c513e67550b6b2ad56c5a4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:35:50.656659Z","signature_b64":"pl4w55PPkY1DfflZEmtcvua42v8GmeIncfnYbciIOHwyNqi2uUtjhV+D837lc7yTLcFdoxDYaEfJJd9AIz3cCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"269675cd1df76e35e2c614990a32462cdf857ad68c513e67550b6b2ad56c5a4c","last_reissued_at":"2026-07-05T06:35:50.656074Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:35:50.656074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.09681","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":"2026-07-05T06:35:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FknK7UP2gY0qhGmDynXB86F3m7lzuE7KknPZCzhnylCImniUhEKLM1JUWfujV8fMY+HWKmojK/TQQBfNtlUSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T21:06:04.368744Z"},"content_sha256":"c1e30673771855bb8d6c01c84d52f875d903abc1b12dab9f6e1e8a1bd48bd4b5","schema_version":"1.0","event_id":"sha256:c1e30673771855bb8d6c01c84d52f875d903abc1b12dab9f6e1e8a1bd48bd4b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:E2LHLTI565XDLYWGCSMQUMSGFT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral flow, twisted modules and MLDE of quasi-lisse vertex algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Bohan Li, Hao Li, WenBin Yan","submitted_at":"2023-04-19T14:19:25Z","abstract_excerpt":"We calculate the fusion rules among $\\mathbb{Z}_2$-twisted modules $L_{\\mathfrak{sl}_2}(\\ell,0)$ at admissible levels. We derive a series MLDEs for normalized characters of ordinary twisted modules of quasi-lisse vertex algebras. Examples include affine VOAs of type $A_1^{(1)}$ at boundary admissible level, admissible level $k=-1/2$, $A^{(1)}_{2}$ at boundary admissible level $k=-3/2$, and $\\mathrm{BP}^{k}$-algebra with special value $k=-9/4$. We also derive characters of some non-vacuum modules for affine VOA of type $D_4$ at non-admissible level $-2$ from spectral flow automorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.09681","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.09681/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":"2026-07-05T06:35:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5t/nY9eIVVBi2OnYtnAypBGfs3N4quM5IDW9nWJ28d7z6RerQiZKFncwWWhHAuooG0HB7fyvyFGorDVQqZUtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T21:06:04.369704Z"},"content_sha256":"b51cab586b5ddc27e64ab88a413c66303f4d351e1bd6f4eb333a411c99d473bc","schema_version":"1.0","event_id":"sha256:b51cab586b5ddc27e64ab88a413c66303f4d351e1bd6f4eb333a411c99d473bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E2LHLTI565XDLYWGCSMQUMSGFT/bundle.json","state_url":"https://pith.science/pith/E2LHLTI565XDLYWGCSMQUMSGFT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E2LHLTI565XDLYWGCSMQUMSGFT/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":"2026-08-12T21:06:04Z","links":{"resolver":"https://pith.science/pith/E2LHLTI565XDLYWGCSMQUMSGFT","bundle":"https://pith.science/pith/E2LHLTI565XDLYWGCSMQUMSGFT/bundle.json","state":"https://pith.science/pith/E2LHLTI565XDLYWGCSMQUMSGFT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E2LHLTI565XDLYWGCSMQUMSGFT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:E2LHLTI565XDLYWGCSMQUMSGFT","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":"3b39d0655718b2f466e05cfaac95f7ac0592531951fe9c3dd2016c21313c27be","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2023-04-19T14:19:25Z","title_canon_sha256":"05a74056c5116f933ebd9ae0d82c9bc03d1ff11c01733ec532afbf4e70bba3e5"},"schema_version":"1.0","source":{"id":"2304.09681","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.09681","created_at":"2026-07-05T06:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"2304.09681v2","created_at":"2026-07-05T06:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.09681","created_at":"2026-07-05T06:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"E2LHLTI565XD","created_at":"2026-07-05T06:35:50Z"},{"alias_kind":"pith_short_16","alias_value":"E2LHLTI565XDLYWG","created_at":"2026-07-05T06:35:50Z"},{"alias_kind":"pith_short_8","alias_value":"E2LHLTI5","created_at":"2026-07-05T06:35:50Z"}],"graph_snapshots":[{"event_id":"sha256:b51cab586b5ddc27e64ab88a413c66303f4d351e1bd6f4eb333a411c99d473bc","target":"graph","created_at":"2026-07-05T06:35:50Z","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/2304.09681/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We calculate the fusion rules among $\\mathbb{Z}_2$-twisted modules $L_{\\mathfrak{sl}_2}(\\ell,0)$ at admissible levels. We derive a series MLDEs for normalized characters of ordinary twisted modules of quasi-lisse vertex algebras. Examples include affine VOAs of type $A_1^{(1)}$ at boundary admissible level, admissible level $k=-1/2$, $A^{(1)}_{2}$ at boundary admissible level $k=-3/2$, and $\\mathrm{BP}^{k}$-algebra with special value $k=-9/4$. We also derive characters of some non-vacuum modules for affine VOA of type $D_4$ at non-admissible level $-2$ from spectral flow automorphism.","authors_text":"Bohan Li, Hao Li, WenBin Yan","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2023-04-19T14:19:25Z","title":"Spectral flow, twisted modules and MLDE of quasi-lisse vertex algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.09681","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:c1e30673771855bb8d6c01c84d52f875d903abc1b12dab9f6e1e8a1bd48bd4b5","target":"record","created_at":"2026-07-05T06:35:50Z","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":"3b39d0655718b2f466e05cfaac95f7ac0592531951fe9c3dd2016c21313c27be","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2023-04-19T14:19:25Z","title_canon_sha256":"05a74056c5116f933ebd9ae0d82c9bc03d1ff11c01733ec532afbf4e70bba3e5"},"schema_version":"1.0","source":{"id":"2304.09681","kind":"arxiv","version":2}},"canonical_sha256":"269675cd1df76e35e2c614990a32462cdf857ad68c513e67550b6b2ad56c5a4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"269675cd1df76e35e2c614990a32462cdf857ad68c513e67550b6b2ad56c5a4c","first_computed_at":"2026-07-05T06:35:50.656074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:35:50.656074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pl4w55PPkY1DfflZEmtcvua42v8GmeIncfnYbciIOHwyNqi2uUtjhV+D837lc7yTLcFdoxDYaEfJJd9AIz3cCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:35:50.656659Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.09681","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e30673771855bb8d6c01c84d52f875d903abc1b12dab9f6e1e8a1bd48bd4b5","sha256:b51cab586b5ddc27e64ab88a413c66303f4d351e1bd6f4eb333a411c99d473bc"],"state_sha256":"409c933731770444d52121b957c3203ae01758335e1efafc14fb978b914e8442"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s9L8Z9UNZse8k8QplIhjcGEzK1pf8FQ3RcmSF2cbNsKRrrdCS2KkWRuYVONURol1tIhPni6o/MKl4yfLaO8tBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T21:06:04.374867Z","bundle_sha256":"baa25ce5959c7d308a6dc352349bb157bed30704108127fb2f8176ada76e220f"}}