{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:J77KIZHKWIBS5PCZ3754JKWONA","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":"fd500a036d22f2e05b8f561a83bbca638be08b8f8a79de6d9d8e770b63aab30a","cross_cats_sorted":["math.MP","math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-02-09T10:17:07Z","title_canon_sha256":"c75471811d7801d3f5309cc8024be0fb4f3cbee76dd925b4e358076cf05064fd"},"schema_version":"1.0","source":{"id":"2102.04742","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.04742","created_at":"2026-07-05T06:45:56Z"},{"alias_kind":"arxiv_version","alias_value":"2102.04742v1","created_at":"2026-07-05T06:45:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.04742","created_at":"2026-07-05T06:45:56Z"},{"alias_kind":"pith_short_12","alias_value":"J77KIZHKWIBS","created_at":"2026-07-05T06:45:56Z"},{"alias_kind":"pith_short_16","alias_value":"J77KIZHKWIBS5PCZ","created_at":"2026-07-05T06:45:56Z"},{"alias_kind":"pith_short_8","alias_value":"J77KIZHK","created_at":"2026-07-05T06:45:56Z"}],"graph_snapshots":[{"event_id":"sha256:c2e2a70805a94fdbba9d607b76ee86630049bcfc284fc24a096b8494ef533924","target":"graph","created_at":"2026-07-05T06:45:56Z","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/2102.04742/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we give Maurer-Cartan characterizations as well as a cohomology theory for compatible Lie algebras. Explicitly, we first introduce the notion of a bidifferential graded Lie algebra and thus give Maurer-Cartan characterizations of compatible Lie algebras. Then we introduce a cohomology theory of compatible Lie algebras and use it to classify infinitesimal deformations and abelian extensions of compatible Lie algebras. In particular, we introduce the reduced cohomology of a compatible Lie algebra and establish the relation between the reduced cohomology of a compatible Lie algebra","authors_text":"Chengming Bai, Jifeng Liu, Yunhe Sheng","cross_cats":["math.MP","math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-02-09T10:17:07Z","title":"Maurer-Cartan characterizations and cohomologies of compatible Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.04742","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":"sha256:6648e2a1a4aaa0907f1d0423d6e9d7d7593feeb96232868b977c75e2ab6471d3","target":"record","created_at":"2026-07-05T06:45:56Z","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":"fd500a036d22f2e05b8f561a83bbca638be08b8f8a79de6d9d8e770b63aab30a","cross_cats_sorted":["math.MP","math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-02-09T10:17:07Z","title_canon_sha256":"c75471811d7801d3f5309cc8024be0fb4f3cbee76dd925b4e358076cf05064fd"},"schema_version":"1.0","source":{"id":"2102.04742","kind":"arxiv","version":1}},"canonical_sha256":"4ffea464eab2032ebc59dffbc4aace68238e49f6440361965a34913450b8ab24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ffea464eab2032ebc59dffbc4aace68238e49f6440361965a34913450b8ab24","first_computed_at":"2026-07-05T06:45:56.079451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:45:56.079451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y3lwqrsUSrIDV1DYhvrjmcndWaRuJHkHiWAs9KZ5t39HKv3zGK4IV/VPxZEHO2fQgXAv24cx2siOPkKkBSegCw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:45:56.079848Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.04742","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6648e2a1a4aaa0907f1d0423d6e9d7d7593feeb96232868b977c75e2ab6471d3","sha256:c2e2a70805a94fdbba9d607b76ee86630049bcfc284fc24a096b8494ef533924"],"state_sha256":"e4c4657a79485adc38c944892739057655d0595eae509a2953c542e9dbb89e61"}