{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:UPLDFQHULJ4EUAAAH62C6QNOWB","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":"215416e7aafca8fcfe431bc3d20bcb9a0d63000f65fe70cd8b3da382c26012b9","cross_cats_sorted":["math.QA","math.RT"],"license":"","primary_cat":"math.DG","submitted_at":"2002-01-15T18:35:59Z","title_canon_sha256":"df127f89f48506e06225e910fd589559912ca840ee699ddb2efc717983f6828e"},"schema_version":"1.0","source":{"id":"math/0201135","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0201135","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0201135v2","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0201135","created_at":"2026-05-18T02:41:33Z"},{"alias_kind":"pith_short_12","alias_value":"UPLDFQHULJ4E","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"UPLDFQHULJ4EUAAA","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"UPLDFQHU","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:775ddbd3dfb1e6aa0efe88024b406b37497a71b39445c891f4ff021c9792128c","target":"graph","created_at":"2026-05-18T02:41:33Z","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"},"paper":{"abstract_excerpt":"We construct bundles of modules of vertex operator algebras, and prove the rigidity and vanishing theorem for the Dirac operator on loop space twisted by such bundles.\n  This result generalizes many previous results.","authors_text":"Chongying Dong, Kefeng Liu, Xiaonan Ma","cross_cats":["math.QA","math.RT"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2002-01-15T18:35:59Z","title":"Elliptic genus and vertex operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0201135","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":"sha256:0d211b6de63e6281e669e78213531934db5f7d2de76cd9adc0e3fd1a9dabee0c","target":"record","created_at":"2026-05-18T02:41:33Z","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":"215416e7aafca8fcfe431bc3d20bcb9a0d63000f65fe70cd8b3da382c26012b9","cross_cats_sorted":["math.QA","math.RT"],"license":"","primary_cat":"math.DG","submitted_at":"2002-01-15T18:35:59Z","title_canon_sha256":"df127f89f48506e06225e910fd589559912ca840ee699ddb2efc717983f6828e"},"schema_version":"1.0","source":{"id":"math/0201135","kind":"arxiv","version":2}},"canonical_sha256":"a3d632c0f45a784a00003fb42f41aeb06e13d1d7924629626b30b4b29e85a6b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3d632c0f45a784a00003fb42f41aeb06e13d1d7924629626b30b4b29e85a6b0","first_computed_at":"2026-05-18T02:41:33.143613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:33.143613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"19ZtrbS3ACPhYGcVPm1EvV12WcTq3moZTgZAevckVkSu+rJGhlPuweaLJfOOEyVHhlFwUdvX9/64AOTheTWwDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:33.144143Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0201135","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d211b6de63e6281e669e78213531934db5f7d2de76cd9adc0e3fd1a9dabee0c","sha256:775ddbd3dfb1e6aa0efe88024b406b37497a71b39445c891f4ff021c9792128c"],"state_sha256":"7cd5219191f84d353e364b41b4f77923a21207d779a5579db8ccfd4bd3d4b160"}