{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:SAFHFIQ2CLVMJY3WWFUVJJZTW6","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":"4064e0b827d960fa95b4f66586d1b8786bff7594ad06cdc511e8611d10291699","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2004-02-26T02:58:57Z","title_canon_sha256":"e1a4d20f4ed3f5efcab838738beda7c0fbbc1c19f481fc4408a9b38f38d411fa"},"schema_version":"1.0","source":{"id":"math/0402421","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0402421","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0402421v1","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402421","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"pith_short_12","alias_value":"SAFHFIQ2CLVM","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"SAFHFIQ2CLVMJY3W","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"SAFHFIQ2","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:f6145ae28bb9dddb384a2663718eb8361650d921e5f9de2b8f1937d64ef2be33","target":"graph","created_at":"2026-05-18T01:38:28Z","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 compute the low dimensional cohomologies $\\tilde H^q(gc_N,C)$, $H^q(gc_N,\\C)$ of the infinite rank general Lie conformal algebras $gc_N$ with trivial coefficients for $q\\le3, N=1$ or $q\\le2, N\\ge2$. We also prove that the cohomology of $gc_N$ with coefficients in its natural module is trivial, i.e., $H^*(gc_N,\\C[\\ptl]^N)=0$; thus partially solve an open problem of Bakalov-Kac-Voronov in [{\\it Comm. Math. Phys.,} {\\bf200} (1999), 561-598].","authors_text":"Yucai Su","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2004-02-26T02:58:57Z","title":"Low dimensional cohomology of general conformal algebras $gc_N$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402421","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":"sha256:54823e703c07590086577da6eeaa90c3ca5204dea2264d530fb79c0806fbe5b6","target":"record","created_at":"2026-05-18T01:38:28Z","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":"4064e0b827d960fa95b4f66586d1b8786bff7594ad06cdc511e8611d10291699","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2004-02-26T02:58:57Z","title_canon_sha256":"e1a4d20f4ed3f5efcab838738beda7c0fbbc1c19f481fc4408a9b38f38d411fa"},"schema_version":"1.0","source":{"id":"math/0402421","kind":"arxiv","version":1}},"canonical_sha256":"900a72a21a12eac4e376b16954a733b7ad23798b6c11ab66343cbb8650610e6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"900a72a21a12eac4e376b16954a733b7ad23798b6c11ab66343cbb8650610e6b","first_computed_at":"2026-05-18T01:38:28.528012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:28.528012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Ggffv25ruWZkGoJIKaot66Fd02ubxfWyLJAdT00b8+7580diSIBD5s/yFuILq5b+DpYGEnAHmS0dpA+34gaCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:28.528650Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0402421","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54823e703c07590086577da6eeaa90c3ca5204dea2264d530fb79c0806fbe5b6","sha256:f6145ae28bb9dddb384a2663718eb8361650d921e5f9de2b8f1937d64ef2be33"],"state_sha256":"f5613b16dfba1b41558d1e0f7471554485b8e2e342e5be74b2e5bb7556639a3e"}