{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:CDKZU7HOKQNOHY3QAYR4NWZIWN","short_pith_number":"pith:CDKZU7HO","canonical_record":{"source":{"id":"math/0302334","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2003-02-26T21:10:17Z","cross_cats_sorted":["math.DG","math.KT"],"title_canon_sha256":"49aad7ec80300f1a077ec8c0d127561544dd3d4a6f75695690e299ab79cec8ac","abstract_canon_sha256":"663b94d38199c1712c550d5d77988d9f0437b4715cedd8ef3816916d11867093"},"schema_version":"1.0"},"canonical_sha256":"10d59a7cee541ae3e3700623c6db28b3476f61c62e295b4419c877bbd0e6e38e","source":{"kind":"arxiv","id":"math/0302334","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0302334","created_at":"2026-05-18T00:17:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0302334v8","created_at":"2026-05-18T00:17:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0302334","created_at":"2026-05-18T00:17:09Z"},{"alias_kind":"pith_short_12","alias_value":"CDKZU7HOKQNO","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"CDKZU7HOKQNOHY3Q","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"CDKZU7HO","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:CDKZU7HOKQNOHY3QAYR4NWZIWN","target":"record","payload":{"canonical_record":{"source":{"id":"math/0302334","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2003-02-26T21:10:17Z","cross_cats_sorted":["math.DG","math.KT"],"title_canon_sha256":"49aad7ec80300f1a077ec8c0d127561544dd3d4a6f75695690e299ab79cec8ac","abstract_canon_sha256":"663b94d38199c1712c550d5d77988d9f0437b4715cedd8ef3816916d11867093"},"schema_version":"1.0"},"canonical_sha256":"10d59a7cee541ae3e3700623c6db28b3476f61c62e295b4419c877bbd0e6e38e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:09.780936Z","signature_b64":"TGajXn9eCVn8e6gVoEPXi4lckWkY+TeNvkkeYuluzqAT/S0I0QzHyhKYtGbNTRJMnO4NsuganS56UfvlYl/hCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10d59a7cee541ae3e3700623c6db28b3476f61c62e295b4419c877bbd0e6e38e","last_reissued_at":"2026-05-18T00:17:09.780197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:09.780197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0302334","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1pPTXMjctCdPzZaMbf/XB/wSmoCuWtGMdHWw12HcSgbLQnkWY2PORu1JE4ndFk3LQ32xBIeEn5Kz7hyXKyhYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:58:44.396305Z"},"content_sha256":"34664c9d2d1fced7dc0439bd7bcfea37f48d9507ec45db94b60c1941fd4c685e","schema_version":"1.0","event_id":"sha256:34664c9d2d1fced7dc0439bd7bcfea37f48d9507ec45db94b60c1941fd4c685e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:CDKZU7HOKQNOHY3QAYR4NWZIWN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low-dimensional cohomology of current Lie algebras and analogs of the Riemann tensor for loop manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.KT"],"primary_cat":"math.RA","authors_text":"Pasha Zusmanovich","submitted_at":"2003-02-26T21:10:17Z","abstract_excerpt":"We obtain formulas for the first and second cohomology groups of a general current Lie algebra with coefficients in the \"current\" module, and apply them to compute structure functions for manifolds of loops with values in compact Hermitian symmetric spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0302334","kind":"arxiv","version":8},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:17:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7FIaYbW52VBOLKmu9d/Hf3DCJngLv3MJPyPuDxCDGSMPc2jZaZNkEeolrUpFfrbZSQSQnADww7PdUE/yS0pJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:58:44.396657Z"},"content_sha256":"90efeaeb2ff8160b3bd87003839fb3988146a8d4b370eba15d2d6f31d70138a0","schema_version":"1.0","event_id":"sha256:90efeaeb2ff8160b3bd87003839fb3988146a8d4b370eba15d2d6f31d70138a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CDKZU7HOKQNOHY3QAYR4NWZIWN/bundle.json","state_url":"https://pith.science/pith/CDKZU7HOKQNOHY3QAYR4NWZIWN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CDKZU7HOKQNOHY3QAYR4NWZIWN/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":"2026-06-26T11:58:44Z","links":{"resolver":"https://pith.science/pith/CDKZU7HOKQNOHY3QAYR4NWZIWN","bundle":"https://pith.science/pith/CDKZU7HOKQNOHY3QAYR4NWZIWN/bundle.json","state":"https://pith.science/pith/CDKZU7HOKQNOHY3QAYR4NWZIWN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CDKZU7HOKQNOHY3QAYR4NWZIWN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:CDKZU7HOKQNOHY3QAYR4NWZIWN","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":"663b94d38199c1712c550d5d77988d9f0437b4715cedd8ef3816916d11867093","cross_cats_sorted":["math.DG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2003-02-26T21:10:17Z","title_canon_sha256":"49aad7ec80300f1a077ec8c0d127561544dd3d4a6f75695690e299ab79cec8ac"},"schema_version":"1.0","source":{"id":"math/0302334","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0302334","created_at":"2026-05-18T00:17:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0302334v8","created_at":"2026-05-18T00:17:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0302334","created_at":"2026-05-18T00:17:09Z"},{"alias_kind":"pith_short_12","alias_value":"CDKZU7HOKQNO","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"CDKZU7HOKQNOHY3Q","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"CDKZU7HO","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:90efeaeb2ff8160b3bd87003839fb3988146a8d4b370eba15d2d6f31d70138a0","target":"graph","created_at":"2026-05-18T00:17:09Z","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 obtain formulas for the first and second cohomology groups of a general current Lie algebra with coefficients in the \"current\" module, and apply them to compute structure functions for manifolds of loops with values in compact Hermitian symmetric spaces.","authors_text":"Pasha Zusmanovich","cross_cats":["math.DG","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2003-02-26T21:10:17Z","title":"Low-dimensional cohomology of current Lie algebras and analogs of the Riemann tensor for loop manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0302334","kind":"arxiv","version":8},"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":"sha256:34664c9d2d1fced7dc0439bd7bcfea37f48d9507ec45db94b60c1941fd4c685e","target":"record","created_at":"2026-05-18T00:17:09Z","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":"663b94d38199c1712c550d5d77988d9f0437b4715cedd8ef3816916d11867093","cross_cats_sorted":["math.DG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2003-02-26T21:10:17Z","title_canon_sha256":"49aad7ec80300f1a077ec8c0d127561544dd3d4a6f75695690e299ab79cec8ac"},"schema_version":"1.0","source":{"id":"math/0302334","kind":"arxiv","version":8}},"canonical_sha256":"10d59a7cee541ae3e3700623c6db28b3476f61c62e295b4419c877bbd0e6e38e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10d59a7cee541ae3e3700623c6db28b3476f61c62e295b4419c877bbd0e6e38e","first_computed_at":"2026-05-18T00:17:09.780197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:09.780197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TGajXn9eCVn8e6gVoEPXi4lckWkY+TeNvkkeYuluzqAT/S0I0QzHyhKYtGbNTRJMnO4NsuganS56UfvlYl/hCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:09.780936Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0302334","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34664c9d2d1fced7dc0439bd7bcfea37f48d9507ec45db94b60c1941fd4c685e","sha256:90efeaeb2ff8160b3bd87003839fb3988146a8d4b370eba15d2d6f31d70138a0"],"state_sha256":"c52c70c64b5a4a6ae1832f4f9a1a48d328cb575ecf88ce983c92dfc3a0d197d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CL6DZ4JP1HouKZK4dM2VOIF+E9VJWb3mHvGTbuT0dHtd6CLUhFJQOrS8KgFuB9u9lIcLRXkTSPH4qYkAEI2vDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:58:44.398555Z","bundle_sha256":"4c38dd9ffbdef4f7230f3601efaa30723f62ed5a4acd246bfd5cfecb9f6443fd"}}