{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:PPMMCCDA4R754ZNRF2JD3D3EW6","short_pith_number":"pith:PPMMCCDA","canonical_record":{"source":{"id":"q-alg/9703016","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1997-03-09T21:16:39Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"15dad4b7bd5673088c8816f512aad5c9e8bb1be327823b50be5750e8d5a2bfb0","abstract_canon_sha256":"d7b7127daf786c3e570859c3c87ec1e3dadfcc0b83e664ff9f8b2679facd6ab8"},"schema_version":"1.0"},"canonical_sha256":"7bd8c10860e47fde65b12e923d8f64b79aab50f146e78a435e192416ff0b07b2","source":{"kind":"arxiv","id":"q-alg/9703016","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9703016","created_at":"2026-07-04T16:06:26Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9703016v2","created_at":"2026-07-04T16:06:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9703016","created_at":"2026-07-04T16:06:26Z"},{"alias_kind":"pith_short_12","alias_value":"PPMMCCDA4R75","created_at":"2026-07-04T16:06:26Z"},{"alias_kind":"pith_short_16","alias_value":"PPMMCCDA4R754ZNR","created_at":"2026-07-04T16:06:26Z"},{"alias_kind":"pith_short_8","alias_value":"PPMMCCDA","created_at":"2026-07-04T16:06:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:PPMMCCDA4R754ZNRF2JD3D3EW6","target":"record","payload":{"canonical_record":{"source":{"id":"q-alg/9703016","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1997-03-09T21:16:39Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"15dad4b7bd5673088c8816f512aad5c9e8bb1be327823b50be5750e8d5a2bfb0","abstract_canon_sha256":"d7b7127daf786c3e570859c3c87ec1e3dadfcc0b83e664ff9f8b2679facd6ab8"},"schema_version":"1.0"},"canonical_sha256":"7bd8c10860e47fde65b12e923d8f64b79aab50f146e78a435e192416ff0b07b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:06:26.586025Z","signature_b64":"LBrk1Le1Sa9kMqOjJ4EbwuN+e2SGhEhWX+HhOlYc2UjT594bLa588wSGqrAuXnNDnAGZLWRSbcDi1bji085GCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bd8c10860e47fde65b12e923d8f64b79aab50f146e78a435e192416ff0b07b2","last_reissued_at":"2026-07-04T16:06:26.585620Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:06:26.585620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"q-alg/9703016","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":"2026-07-04T16:06:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F4Q65tHgOMvkPuWyKotkSUr5pj8apHKOdx+j67zlPP1rwAWrvxDhOjOTVrSo1vqpAjV/4nnINDfHRjfPDEXwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T16:43:56.003467Z"},"content_sha256":"e2675628793901ca6c859eebade473a234b724c9bd855a373e6fd4cde0b85c16","schema_version":"1.0","event_id":"sha256:e2675628793901ca6c859eebade473a234b724c9bd855a373e6fd4cde0b85c16"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:PPMMCCDA4R754ZNRF2JD3D3EW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular invariance of trace functions in orbifold theory","license":"","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"q-alg","authors_text":"Chongying Dong, Geoffrey Mason, Haisheng Li","submitted_at":"1997-03-09T21:16:39Z","abstract_excerpt":"The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of rational orbifold conformal field theory, in other words the theory of rational vertex operator algebras and their automorphisms. Under a certain finiteness condition on a rational vertex operator algebra V which holds in all known examples, we determine the precise numbers of g-twisted sectors for any automorphism g of V of finite order. We prove that the trace functions and correlations functions associated with such twisted sectors are holomorphic functions in the upper half-plane and, und"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9703016","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/q-alg/9703016/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":"2026-07-04T16:06:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+mS+1sKCXZytQY+ZRwWi32dWEuGYQwHeRM1qMY5V2Jqz+kxAU2+Ol2OB0YuI1ojNzuK4RLLJnfS5vQwX5GJGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T16:43:56.004045Z"},"content_sha256":"3f25a3c9f73975bc4621239c9af32b7de708f875be8a93d907c29f8220a217e6","schema_version":"1.0","event_id":"sha256:3f25a3c9f73975bc4621239c9af32b7de708f875be8a93d907c29f8220a217e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PPMMCCDA4R754ZNRF2JD3D3EW6/bundle.json","state_url":"https://pith.science/pith/PPMMCCDA4R754ZNRF2JD3D3EW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PPMMCCDA4R754ZNRF2JD3D3EW6/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":"2026-08-21T16:43:56Z","links":{"resolver":"https://pith.science/pith/PPMMCCDA4R754ZNRF2JD3D3EW6","bundle":"https://pith.science/pith/PPMMCCDA4R754ZNRF2JD3D3EW6/bundle.json","state":"https://pith.science/pith/PPMMCCDA4R754ZNRF2JD3D3EW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PPMMCCDA4R754ZNRF2JD3D3EW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:PPMMCCDA4R754ZNRF2JD3D3EW6","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":"d7b7127daf786c3e570859c3c87ec1e3dadfcc0b83e664ff9f8b2679facd6ab8","cross_cats_sorted":["hep-th","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1997-03-09T21:16:39Z","title_canon_sha256":"15dad4b7bd5673088c8816f512aad5c9e8bb1be327823b50be5750e8d5a2bfb0"},"schema_version":"1.0","source":{"id":"q-alg/9703016","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9703016","created_at":"2026-07-04T16:06:26Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9703016v2","created_at":"2026-07-04T16:06:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9703016","created_at":"2026-07-04T16:06:26Z"},{"alias_kind":"pith_short_12","alias_value":"PPMMCCDA4R75","created_at":"2026-07-04T16:06:26Z"},{"alias_kind":"pith_short_16","alias_value":"PPMMCCDA4R754ZNR","created_at":"2026-07-04T16:06:26Z"},{"alias_kind":"pith_short_8","alias_value":"PPMMCCDA","created_at":"2026-07-04T16:06:26Z"}],"graph_snapshots":[{"event_id":"sha256:3f25a3c9f73975bc4621239c9af32b7de708f875be8a93d907c29f8220a217e6","target":"graph","created_at":"2026-07-04T16:06:26Z","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/9703016/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of rational orbifold conformal field theory, in other words the theory of rational vertex operator algebras and their automorphisms. Under a certain finiteness condition on a rational vertex operator algebra V which holds in all known examples, we determine the precise numbers of g-twisted sectors for any automorphism g of V of finite order. We prove that the trace functions and correlations functions associated with such twisted sectors are holomorphic functions in the upper half-plane and, und","authors_text":"Chongying Dong, Geoffrey Mason, Haisheng Li","cross_cats":["hep-th","math.QA"],"headline":"","license":"","primary_cat":"q-alg","submitted_at":"1997-03-09T21:16:39Z","title":"Modular invariance of trace functions in orbifold theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9703016","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:e2675628793901ca6c859eebade473a234b724c9bd855a373e6fd4cde0b85c16","target":"record","created_at":"2026-07-04T16:06:26Z","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":"d7b7127daf786c3e570859c3c87ec1e3dadfcc0b83e664ff9f8b2679facd6ab8","cross_cats_sorted":["hep-th","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1997-03-09T21:16:39Z","title_canon_sha256":"15dad4b7bd5673088c8816f512aad5c9e8bb1be327823b50be5750e8d5a2bfb0"},"schema_version":"1.0","source":{"id":"q-alg/9703016","kind":"arxiv","version":2}},"canonical_sha256":"7bd8c10860e47fde65b12e923d8f64b79aab50f146e78a435e192416ff0b07b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bd8c10860e47fde65b12e923d8f64b79aab50f146e78a435e192416ff0b07b2","first_computed_at":"2026-07-04T16:06:26.585620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:06:26.585620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LBrk1Le1Sa9kMqOjJ4EbwuN+e2SGhEhWX+HhOlYc2UjT594bLa588wSGqrAuXnNDnAGZLWRSbcDi1bji085GCA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:06:26.586025Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-alg/9703016","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2675628793901ca6c859eebade473a234b724c9bd855a373e6fd4cde0b85c16","sha256:3f25a3c9f73975bc4621239c9af32b7de708f875be8a93d907c29f8220a217e6"],"state_sha256":"06f4ee82706e6073e667da3c2583a52049eaf77d7a6ad27971f81e7a6720ad83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T24wvQnj6/kBFnbnsdAcplMH/aAU5zYiDPBQz9xxdrYlv2mxIkfDKHM/ic7Ms1ekXh1UTDbZfHfwG6WTUhOgAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T16:43:56.009207Z","bundle_sha256":"2395550702c2dead1979bf1ad47174d0e7b0d05a3eae771a9d808f871e084f67"}}