{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:DIHVU6OP77BNP7KXPZJWNCTNUC","short_pith_number":"pith:DIHVU6OP","canonical_record":{"source":{"id":"q-alg/9509005","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1995-09-06T19:48:15Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"8ac7936ca1623c72f78d3636363e02059b07ca7917c2678e3943550f8d13bbc5","abstract_canon_sha256":"9062d2c6915bab7ff7d59b9ff102de8b9263782f15405b50daf349725a26b8fb"},"schema_version":"1.0"},"canonical_sha256":"1a0f5a79cfffc2d7fd577e53668a6da08c7c0406746c557bc9c4e24a7b81dc98","source":{"kind":"arxiv","id":"q-alg/9509005","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9509005","created_at":"2026-07-04T15:09:06Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9509005v1","created_at":"2026-07-04T15:09:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9509005","created_at":"2026-07-04T15:09:06Z"},{"alias_kind":"pith_short_12","alias_value":"DIHVU6OP77BN","created_at":"2026-07-04T15:09:06Z"},{"alias_kind":"pith_short_16","alias_value":"DIHVU6OP77BNP7KX","created_at":"2026-07-04T15:09:06Z"},{"alias_kind":"pith_short_8","alias_value":"DIHVU6OP","created_at":"2026-07-04T15:09:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:DIHVU6OP77BNP7KXPZJWNCTNUC","target":"record","payload":{"canonical_record":{"source":{"id":"q-alg/9509005","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1995-09-06T19:48:15Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"8ac7936ca1623c72f78d3636363e02059b07ca7917c2678e3943550f8d13bbc5","abstract_canon_sha256":"9062d2c6915bab7ff7d59b9ff102de8b9263782f15405b50daf349725a26b8fb"},"schema_version":"1.0"},"canonical_sha256":"1a0f5a79cfffc2d7fd577e53668a6da08c7c0406746c557bc9c4e24a7b81dc98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:09:06.467533Z","signature_b64":"Caff7SrT+wqsY+3k2EJ6WkZ/Fqcl2lrqUseLK+xHHuljF5HRg6UwT2xbo/tXqQM0keXijhrGjaB97rgpx2zfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a0f5a79cfffc2d7fd577e53668a6da08c7c0406746c557bc9c4e24a7b81dc98","last_reissued_at":"2026-07-04T15:09:06.467145Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:09:06.467145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"q-alg/9509005","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:09:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8SUiqTSdLZQzVyeTT92GfgBYqxgnU6RgYT+SpcO7D7/wDe6VifI4iY2lToIY1YmIfrLqrLDIL671DNUWR2z8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T02:25:34.904865Z"},"content_sha256":"82ddd778017a4fc8f4f47e54780ecf326a060a5f10d0376e1353da44a3ef6e17","schema_version":"1.0","event_id":"sha256:82ddd778017a4fc8f4f47e54780ecf326a060a5f10d0376e1353da44a3ef6e17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:DIHVU6OP77BNP7KXPZJWNCTNUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted representations of vertex operator algebras","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"q-alg","authors_text":"Chongying Dong, Geoffrey Mason, Haisheng Li","submitted_at":"1995-09-06T19:48:15Z","abstract_excerpt":"Let $V$ be a vertex operator algebra and $g$ an automorphism of finite order. We construct an associative algebra $A_g(V)$ and a pair of functors between the category of $A_g(V)$-modules and a certain category of admissible $g$-twisted $V$-modules. In particular, these functors exhibit a bijection between the simple modules in each category. We give various applications, including the fact that the complete reducibility of admissible $g$-twisted modules implies both the finite-dimensionality of homogeneous spaces and the finiteness of the number of simple $g$-twisted modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9509005","kind":"arxiv","version":1},"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/q-alg/9509005/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":"2026-07-04T15:09:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4R7C5cKnjBViV/eoW4dwxXcvG5siy2HEjEx0iB+4ioIHU/Rmg9ugmmHy3Dw69/5OZ1dMRtuigeMgYdE/auwLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T02:25:34.905159Z"},"content_sha256":"852a019a1d11e7bebfedf0725db219b214892da304fb6a49ac76910bbead56e2","schema_version":"1.0","event_id":"sha256:852a019a1d11e7bebfedf0725db219b214892da304fb6a49ac76910bbead56e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DIHVU6OP77BNP7KXPZJWNCTNUC/bundle.json","state_url":"https://pith.science/pith/DIHVU6OP77BNP7KXPZJWNCTNUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DIHVU6OP77BNP7KXPZJWNCTNUC/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":"2026-08-01T02:25:34Z","links":{"resolver":"https://pith.science/pith/DIHVU6OP77BNP7KXPZJWNCTNUC","bundle":"https://pith.science/pith/DIHVU6OP77BNP7KXPZJWNCTNUC/bundle.json","state":"https://pith.science/pith/DIHVU6OP77BNP7KXPZJWNCTNUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DIHVU6OP77BNP7KXPZJWNCTNUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:DIHVU6OP77BNP7KXPZJWNCTNUC","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":"9062d2c6915bab7ff7d59b9ff102de8b9263782f15405b50daf349725a26b8fb","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1995-09-06T19:48:15Z","title_canon_sha256":"8ac7936ca1623c72f78d3636363e02059b07ca7917c2678e3943550f8d13bbc5"},"schema_version":"1.0","source":{"id":"q-alg/9509005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9509005","created_at":"2026-07-04T15:09:06Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9509005v1","created_at":"2026-07-04T15:09:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9509005","created_at":"2026-07-04T15:09:06Z"},{"alias_kind":"pith_short_12","alias_value":"DIHVU6OP77BN","created_at":"2026-07-04T15:09:06Z"},{"alias_kind":"pith_short_16","alias_value":"DIHVU6OP77BNP7KX","created_at":"2026-07-04T15:09:06Z"},{"alias_kind":"pith_short_8","alias_value":"DIHVU6OP","created_at":"2026-07-04T15:09:06Z"}],"graph_snapshots":[{"event_id":"sha256:852a019a1d11e7bebfedf0725db219b214892da304fb6a49ac76910bbead56e2","target":"graph","created_at":"2026-07-04T15:09:06Z","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/q-alg/9509005/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 and $g$ an automorphism of finite order. We construct an associative algebra $A_g(V)$ and a pair of functors between the category of $A_g(V)$-modules and a certain category of admissible $g$-twisted $V$-modules. In particular, these functors exhibit a bijection between the simple modules in each category. We give various applications, including the fact that the complete reducibility of admissible $g$-twisted modules implies both the finite-dimensionality of homogeneous spaces and the finiteness of the number of simple $g$-twisted modules.","authors_text":"Chongying Dong, Geoffrey Mason, Haisheng Li","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"q-alg","submitted_at":"1995-09-06T19:48:15Z","title":"Twisted representations of vertex operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9509005","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":"sha256:82ddd778017a4fc8f4f47e54780ecf326a060a5f10d0376e1353da44a3ef6e17","target":"record","created_at":"2026-07-04T15:09:06Z","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":"9062d2c6915bab7ff7d59b9ff102de8b9263782f15405b50daf349725a26b8fb","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1995-09-06T19:48:15Z","title_canon_sha256":"8ac7936ca1623c72f78d3636363e02059b07ca7917c2678e3943550f8d13bbc5"},"schema_version":"1.0","source":{"id":"q-alg/9509005","kind":"arxiv","version":1}},"canonical_sha256":"1a0f5a79cfffc2d7fd577e53668a6da08c7c0406746c557bc9c4e24a7b81dc98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a0f5a79cfffc2d7fd577e53668a6da08c7c0406746c557bc9c4e24a7b81dc98","first_computed_at":"2026-07-04T15:09:06.467145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:09:06.467145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Caff7SrT+wqsY+3k2EJ6WkZ/Fqcl2lrqUseLK+xHHuljF5HRg6UwT2xbo/tXqQM0keXijhrGjaB97rgpx2zfAg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:09:06.467533Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-alg/9509005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82ddd778017a4fc8f4f47e54780ecf326a060a5f10d0376e1353da44a3ef6e17","sha256:852a019a1d11e7bebfedf0725db219b214892da304fb6a49ac76910bbead56e2"],"state_sha256":"34edf10aa36077dd2dc3b6495d483e0c3c3c6098c65b347ecd47ea79b9c6cc63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UaDJhScCT0dym4lGPhh0p7+h/KDt7ttf/zLMBR2YF8SIzvTqAKEgjt9xO2rGJ5bJEzhJ9+b1KKtutiZU8309Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T02:25:34.907645Z","bundle_sha256":"4733a83db9d1993f88e289ec4c8f12b5edec51d7b7ff05956c107fa9fdaced34"}}