{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:BDRONCOGKOG2RYFHD2JQWHCAHB","short_pith_number":"pith:BDRONCOG","canonical_record":{"source":{"id":"math/0210274","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2002-10-17T20:03:48Z","cross_cats_sorted":[],"title_canon_sha256":"1eb7f616b22eef120490f0c565f4527c4df7868096e0fcaa6bbdc9dadc15a860","abstract_canon_sha256":"20fb19a179c83925a5afdf670664d06d0f011f8b136a0e78ae7a4f62fcc46e51"},"schema_version":"1.0"},"canonical_sha256":"08e2e689c6538da8e0a71e930b1c403866bcd2d280a2c0d5926884fa9ca4c7a5","source":{"kind":"arxiv","id":"math/0210274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0210274","created_at":"2026-07-04T14:36:39Z"},{"alias_kind":"arxiv_version","alias_value":"math/0210274v1","created_at":"2026-07-04T14:36:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0210274","created_at":"2026-07-04T14:36:39Z"},{"alias_kind":"pith_short_12","alias_value":"BDRONCOGKOG2","created_at":"2026-07-04T14:36:39Z"},{"alias_kind":"pith_short_16","alias_value":"BDRONCOGKOG2RYFH","created_at":"2026-07-04T14:36:39Z"},{"alias_kind":"pith_short_8","alias_value":"BDRONCOG","created_at":"2026-07-04T14:36:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:BDRONCOGKOG2RYFHD2JQWHCAHB","target":"record","payload":{"canonical_record":{"source":{"id":"math/0210274","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2002-10-17T20:03:48Z","cross_cats_sorted":[],"title_canon_sha256":"1eb7f616b22eef120490f0c565f4527c4df7868096e0fcaa6bbdc9dadc15a860","abstract_canon_sha256":"20fb19a179c83925a5afdf670664d06d0f011f8b136a0e78ae7a4f62fcc46e51"},"schema_version":"1.0"},"canonical_sha256":"08e2e689c6538da8e0a71e930b1c403866bcd2d280a2c0d5926884fa9ca4c7a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:36:39.088898Z","signature_b64":"3Pjvf+RYTSpd6srYDOms9JCm0cN6xGBTVwsWOQwJvrKThvu/2OQk4YSOLozI/KxFkt1DbrbIsVmy/hAz+9NyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08e2e689c6538da8e0a71e930b1c403866bcd2d280a2c0d5926884fa9ca4c7a5","last_reissued_at":"2026-07-04T14:36:39.088496Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:36:39.088496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0210274","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":"2026-07-04T14:36:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VLzeQnO9hGaECwcrgvqeY9oIvkQH5bXaXbBhVAYKSHILM1aX4Xjem2IdViPmZGVqwEn6MQ40vBJmnN+26oGvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T14:48:59.311698Z"},"content_sha256":"44edaddbe9897d41cdb68f25cd200fb51e0e8e2221129c99e0a5f0e6ac6d8737","schema_version":"1.0","event_id":"sha256:44edaddbe9897d41cdb68f25cd200fb51e0e8e2221129c99e0a5f0e6ac6d8737"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:BDRONCOGKOG2RYFHD2JQWHCAHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of irreducible modules for the vertex operator algebra V_L^+: General case","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"C. Dong, T. Abe","submitted_at":"2002-10-17T20:03:48Z","abstract_excerpt":"The irreducible modules for the fixed point vertex operator subalgebra V_L^+ of the vertex operator algebra V_L associated to an arbitrary positive definite even lattice L under the automorphism lifted from the -1 isometry of L are classified."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210274","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/math/0210274/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":"2026-07-04T14:36:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xK1tN4jdw5yhTXVtl3RWge6VhtWR2FjD9GH0ECc1P2mocSFNO7kOnScRAnJhnWuXigmj56YWC7u16oHxulykCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T14:48:59.312120Z"},"content_sha256":"8a407216453bad864c93e0dd01d268cfce94182dfdd4daa6772634ad370e0f51","schema_version":"1.0","event_id":"sha256:8a407216453bad864c93e0dd01d268cfce94182dfdd4daa6772634ad370e0f51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDRONCOGKOG2RYFHD2JQWHCAHB/bundle.json","state_url":"https://pith.science/pith/BDRONCOGKOG2RYFHD2JQWHCAHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDRONCOGKOG2RYFHD2JQWHCAHB/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":"2026-07-08T14:48:59Z","links":{"resolver":"https://pith.science/pith/BDRONCOGKOG2RYFHD2JQWHCAHB","bundle":"https://pith.science/pith/BDRONCOGKOG2RYFHD2JQWHCAHB/bundle.json","state":"https://pith.science/pith/BDRONCOGKOG2RYFHD2JQWHCAHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDRONCOGKOG2RYFHD2JQWHCAHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:BDRONCOGKOG2RYFHD2JQWHCAHB","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":"20fb19a179c83925a5afdf670664d06d0f011f8b136a0e78ae7a4f62fcc46e51","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2002-10-17T20:03:48Z","title_canon_sha256":"1eb7f616b22eef120490f0c565f4527c4df7868096e0fcaa6bbdc9dadc15a860"},"schema_version":"1.0","source":{"id":"math/0210274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0210274","created_at":"2026-07-04T14:36:39Z"},{"alias_kind":"arxiv_version","alias_value":"math/0210274v1","created_at":"2026-07-04T14:36:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0210274","created_at":"2026-07-04T14:36:39Z"},{"alias_kind":"pith_short_12","alias_value":"BDRONCOGKOG2","created_at":"2026-07-04T14:36:39Z"},{"alias_kind":"pith_short_16","alias_value":"BDRONCOGKOG2RYFH","created_at":"2026-07-04T14:36:39Z"},{"alias_kind":"pith_short_8","alias_value":"BDRONCOG","created_at":"2026-07-04T14:36:39Z"}],"graph_snapshots":[{"event_id":"sha256:8a407216453bad864c93e0dd01d268cfce94182dfdd4daa6772634ad370e0f51","target":"graph","created_at":"2026-07-04T14:36:39Z","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/math/0210274/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The irreducible modules for the fixed point vertex operator subalgebra V_L^+ of the vertex operator algebra V_L associated to an arbitrary positive definite even lattice L under the automorphism lifted from the -1 isometry of L are classified.","authors_text":"C. Dong, T. Abe","cross_cats":[],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2002-10-17T20:03:48Z","title":"Classification of irreducible modules for the vertex operator algebra V_L^+: General case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0210274","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":"sha256:44edaddbe9897d41cdb68f25cd200fb51e0e8e2221129c99e0a5f0e6ac6d8737","target":"record","created_at":"2026-07-04T14:36:39Z","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":"20fb19a179c83925a5afdf670664d06d0f011f8b136a0e78ae7a4f62fcc46e51","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2002-10-17T20:03:48Z","title_canon_sha256":"1eb7f616b22eef120490f0c565f4527c4df7868096e0fcaa6bbdc9dadc15a860"},"schema_version":"1.0","source":{"id":"math/0210274","kind":"arxiv","version":1}},"canonical_sha256":"08e2e689c6538da8e0a71e930b1c403866bcd2d280a2c0d5926884fa9ca4c7a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08e2e689c6538da8e0a71e930b1c403866bcd2d280a2c0d5926884fa9ca4c7a5","first_computed_at":"2026-07-04T14:36:39.088496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:39.088496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Pjvf+RYTSpd6srYDOms9JCm0cN6xGBTVwsWOQwJvrKThvu/2OQk4YSOLozI/KxFkt1DbrbIsVmy/hAz+9NyDg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:39.088898Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0210274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44edaddbe9897d41cdb68f25cd200fb51e0e8e2221129c99e0a5f0e6ac6d8737","sha256:8a407216453bad864c93e0dd01d268cfce94182dfdd4daa6772634ad370e0f51"],"state_sha256":"0f04e435fae939b85a15132c15a2aa0aab13cb63b9824f82526921fab157ccb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9l0t9b6/9oqjtb96oxyE6PNHwMYbSaHNC3MbO7MqtgLmGmPkxZlEuJ+ayzxUrpMzvgp/vZjcH65KGcHA5XYDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T14:48:59.314234Z","bundle_sha256":"c8b191f2f341d5c783c5e60cc7441d0b99c239161b30c3d7b511d89dd57322c8"}}