{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FTDDWXAKNE4KGTJMPMBBMIOV7S","short_pith_number":"pith:FTDDWXAK","canonical_record":{"source":{"id":"1705.05017","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-14T19:08:07Z","cross_cats_sorted":["math-ph","math.CT","math.MP","math.RT"],"title_canon_sha256":"2d7051d7e6183fc26a6ec7debc8a52c0206dbaadbb15ed9b545bb023c3e8ee4a","abstract_canon_sha256":"15b3b6f8ed1a765f3bdb73a1e5e2fc3c4dd953bc3cc3df08e32ff0932d1dcdca"},"schema_version":"1.0"},"canonical_sha256":"2cc63b5c0a6938a34d2c7b021621d5fcb56e6d1c89ecbe69bebcfe6dec4426d9","source":{"kind":"arxiv","id":"1705.05017","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05017","created_at":"2026-07-05T08:02:39Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05017v2","created_at":"2026-07-05T08:02:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05017","created_at":"2026-07-05T08:02:39Z"},{"alias_kind":"pith_short_12","alias_value":"FTDDWXAKNE4K","created_at":"2026-07-05T08:02:39Z"},{"alias_kind":"pith_short_16","alias_value":"FTDDWXAKNE4KGTJM","created_at":"2026-07-05T08:02:39Z"},{"alias_kind":"pith_short_8","alias_value":"FTDDWXAK","created_at":"2026-07-05T08:02:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FTDDWXAKNE4KGTJMPMBBMIOV7S","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05017","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-14T19:08:07Z","cross_cats_sorted":["math-ph","math.CT","math.MP","math.RT"],"title_canon_sha256":"2d7051d7e6183fc26a6ec7debc8a52c0206dbaadbb15ed9b545bb023c3e8ee4a","abstract_canon_sha256":"15b3b6f8ed1a765f3bdb73a1e5e2fc3c4dd953bc3cc3df08e32ff0932d1dcdca"},"schema_version":"1.0"},"canonical_sha256":"2cc63b5c0a6938a34d2c7b021621d5fcb56e6d1c89ecbe69bebcfe6dec4426d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:02:39.704023Z","signature_b64":"E4ubbqhc0VnyhvwlXCsTe2J5Y7kGqGua28ujMSQamsjB30E2yYWaQY+ZNmgB5c7AvhNfPBQg9aexGTOWZFWKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cc63b5c0a6938a34d2c7b021621d5fcb56e6d1c89ecbe69bebcfe6dec4426d9","last_reissued_at":"2026-07-05T08:02:39.703576Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:02:39.703576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05017","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":"2026-07-05T08:02:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lX/RAyY3VyIDp94+jjEJAByKXwN9HizfXHQH49EJlD+gOPOmz6+qfRbeUJMTZPzuhqn7WEQvEvDNZcEgFaGIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:22:59.696688Z"},"content_sha256":"bf3a4e4e46472a6b490e09185273ba6cea9a09ea98f4fa066fe7981de34a0bac","schema_version":"1.0","event_id":"sha256:bf3a4e4e46472a6b490e09185273ba6cea9a09ea98f4fa066fe7981de34a0bac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FTDDWXAKNE4KGTJMPMBBMIOV7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor categories for vertex operator superalgebra extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CT","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Robert McRae, Shashank Kanade, Thomas Creutzig","submitted_at":"2017-05-14T19:08:07Z","abstract_excerpt":"Let $V$ be a vertex operator algebra with a category $\\mathcal{C}$ of (generalized) modules that has vertex tensor category structure, and thus braided tensor category structure, and let $A$ be a vertex operator (super)algebra extension of $V$. We employ tensor categories to study untwisted (also called local) $A$-modules in $\\mathcal{C}$, using results of Huang-Kirillov-Lepowsky showing that $A$ is a (super)algebra object in $\\mathcal{C}$ and that generalized $A$-modules in $\\mathcal{C}$ correspond exactly to local modules for the corresponding (super)algebra object. Both categories, of local"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05017","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/1705.05017/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":"2026-07-05T08:02:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"boHikYl2//x+5u5a1H/OAKA9nRf/uXLnKRG6gO6mc+eqZjROTReDkXM+aNFZ7zhIrBgIY0Es2Ap9U+EW4Gr0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:22:59.697393Z"},"content_sha256":"77ca8aad43ed187b8dabb6985e5a28a2dee0f966462769df5e42f7d2cea4cb26","schema_version":"1.0","event_id":"sha256:77ca8aad43ed187b8dabb6985e5a28a2dee0f966462769df5e42f7d2cea4cb26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FTDDWXAKNE4KGTJMPMBBMIOV7S/bundle.json","state_url":"https://pith.science/pith/FTDDWXAKNE4KGTJMPMBBMIOV7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FTDDWXAKNE4KGTJMPMBBMIOV7S/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":"2026-08-13T21:22:59Z","links":{"resolver":"https://pith.science/pith/FTDDWXAKNE4KGTJMPMBBMIOV7S","bundle":"https://pith.science/pith/FTDDWXAKNE4KGTJMPMBBMIOV7S/bundle.json","state":"https://pith.science/pith/FTDDWXAKNE4KGTJMPMBBMIOV7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FTDDWXAKNE4KGTJMPMBBMIOV7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FTDDWXAKNE4KGTJMPMBBMIOV7S","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":"15b3b6f8ed1a765f3bdb73a1e5e2fc3c4dd953bc3cc3df08e32ff0932d1dcdca","cross_cats_sorted":["math-ph","math.CT","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-14T19:08:07Z","title_canon_sha256":"2d7051d7e6183fc26a6ec7debc8a52c0206dbaadbb15ed9b545bb023c3e8ee4a"},"schema_version":"1.0","source":{"id":"1705.05017","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05017","created_at":"2026-07-05T08:02:39Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05017v2","created_at":"2026-07-05T08:02:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05017","created_at":"2026-07-05T08:02:39Z"},{"alias_kind":"pith_short_12","alias_value":"FTDDWXAKNE4K","created_at":"2026-07-05T08:02:39Z"},{"alias_kind":"pith_short_16","alias_value":"FTDDWXAKNE4KGTJM","created_at":"2026-07-05T08:02:39Z"},{"alias_kind":"pith_short_8","alias_value":"FTDDWXAK","created_at":"2026-07-05T08:02:39Z"}],"graph_snapshots":[{"event_id":"sha256:77ca8aad43ed187b8dabb6985e5a28a2dee0f966462769df5e42f7d2cea4cb26","target":"graph","created_at":"2026-07-05T08:02:39Z","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/1705.05017/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $V$ be a vertex operator algebra with a category $\\mathcal{C}$ of (generalized) modules that has vertex tensor category structure, and thus braided tensor category structure, and let $A$ be a vertex operator (super)algebra extension of $V$. We employ tensor categories to study untwisted (also called local) $A$-modules in $\\mathcal{C}$, using results of Huang-Kirillov-Lepowsky showing that $A$ is a (super)algebra object in $\\mathcal{C}$ and that generalized $A$-modules in $\\mathcal{C}$ correspond exactly to local modules for the corresponding (super)algebra object. Both categories, of local","authors_text":"Robert McRae, Shashank Kanade, Thomas Creutzig","cross_cats":["math-ph","math.CT","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-14T19:08:07Z","title":"Tensor categories for vertex operator superalgebra extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05017","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:bf3a4e4e46472a6b490e09185273ba6cea9a09ea98f4fa066fe7981de34a0bac","target":"record","created_at":"2026-07-05T08:02:39Z","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":"15b3b6f8ed1a765f3bdb73a1e5e2fc3c4dd953bc3cc3df08e32ff0932d1dcdca","cross_cats_sorted":["math-ph","math.CT","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-14T19:08:07Z","title_canon_sha256":"2d7051d7e6183fc26a6ec7debc8a52c0206dbaadbb15ed9b545bb023c3e8ee4a"},"schema_version":"1.0","source":{"id":"1705.05017","kind":"arxiv","version":2}},"canonical_sha256":"2cc63b5c0a6938a34d2c7b021621d5fcb56e6d1c89ecbe69bebcfe6dec4426d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cc63b5c0a6938a34d2c7b021621d5fcb56e6d1c89ecbe69bebcfe6dec4426d9","first_computed_at":"2026-07-05T08:02:39.703576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:02:39.703576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E4ubbqhc0VnyhvwlXCsTe2J5Y7kGqGua28ujMSQamsjB30E2yYWaQY+ZNmgB5c7AvhNfPBQg9aexGTOWZFWKBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:02:39.704023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05017","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf3a4e4e46472a6b490e09185273ba6cea9a09ea98f4fa066fe7981de34a0bac","sha256:77ca8aad43ed187b8dabb6985e5a28a2dee0f966462769df5e42f7d2cea4cb26"],"state_sha256":"955e67a9949476ac08d3f1dab82e4c4309df2f333d57cd1161a9c088c722eb68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tD/aG2UOp1PHYGAidcmrSRREbb/nNzrZJJsy5s3RadCcuQVrFh4Pm9Nun5qzlvwCjHsV3fEUHZIKUD4fVCw4DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T21:22:59.707803Z","bundle_sha256":"8053884d18209d28eaa5416858dfb6033cc92bebe091ea5af99ed865d279475f"}}