{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:2O5WDJSRKPUSKIXR66RGSJI3PO","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":"f7098b393924ac0031008dd484a89984bffcd973ee10424656f42144eeedb966","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-11-29T14:55:34Z","title_canon_sha256":"dbe48a42cc50114691d867f0bdd02ba283f2eb42adbe5defe2f867c917393e9f"},"schema_version":"1.0","source":{"id":"0812.0080","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0080","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0080v3","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0080","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"pith_short_12","alias_value":"2O5WDJSRKPUS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"2O5WDJSRKPUSKIXR","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"2O5WDJSR","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:c5542e76b565e3654af802ff45ed5c2ac177f7be141d4fe3f917c98e6a07b042","target":"graph","created_at":"2026-05-18T03:31:07Z","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 study a certain generalization of Lie algebras where the Jacobian of three elements does not vanish but is equal to an expression depending on a skew-symmetric bilinear form.","authors_text":"Pasha Zusmanovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-11-29T14:55:34Z","title":"$\\omega$-Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0080","kind":"arxiv","version":3},"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":"sha256:48c9bd9db839701e0bd891cbdcef79df18703005a101cc4a9b576ed885a756f4","target":"record","created_at":"2026-05-18T03:31:07Z","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":"f7098b393924ac0031008dd484a89984bffcd973ee10424656f42144eeedb966","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-11-29T14:55:34Z","title_canon_sha256":"dbe48a42cc50114691d867f0bdd02ba283f2eb42adbe5defe2f867c917393e9f"},"schema_version":"1.0","source":{"id":"0812.0080","kind":"arxiv","version":3}},"canonical_sha256":"d3bb61a65153e92522f1f7a269251b7b913cf4f4156743d5ad95b3ca32af1a0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3bb61a65153e92522f1f7a269251b7b913cf4f4156743d5ad95b3ca32af1a0f","first_computed_at":"2026-05-18T03:31:07.266561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:07.266561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zjXSP2E2iqAJo4S9WnrKTNvAcOyCZPUzrkIfaT8I5MYkiwgpe+OTF3RBej31bZnXk/OWxGA3Gh38QakJNOpJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:07.267194Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.0080","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48c9bd9db839701e0bd891cbdcef79df18703005a101cc4a9b576ed885a756f4","sha256:c5542e76b565e3654af802ff45ed5c2ac177f7be141d4fe3f917c98e6a07b042"],"state_sha256":"51c498803e0ffacb861df6eb7f73197081ee5c1f3335f960b4401461c956fe21"}