{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DOZ2D3LYKQLBDGSD3PSSDPQ73O","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":"84cf3844e2f8aa50442d6a83d9b41a47bd5c2f85192ad629808cefd8cfc49476","cross_cats_sorted":["math.DG","math.RA","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-06-06T08:27:29Z","title_canon_sha256":"e3ab12faec2a1160cfebacc784e831bff86d21b4360b66cdd23c62178d1c8754"},"schema_version":"1.0","source":{"id":"1606.01654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01654","created_at":"2026-05-18T01:12:53Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01654v1","created_at":"2026-05-18T01:12:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01654","created_at":"2026-05-18T01:12:53Z"},{"alias_kind":"pith_short_12","alias_value":"DOZ2D3LYKQLB","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DOZ2D3LYKQLBDGSD","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DOZ2D3LY","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:e77594f72332ca0dba10de07c384b3adc801f7c21798a398ad032ee5ce41f0b6","target":"graph","created_at":"2026-05-18T01:12:53Z","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":"In this note we define a notion of Courant pair as a Courant algebra over the Lie algebra of linear derivations on an associative algebra. We study formal deformations of Courant pairs by constructing a cohomology bicomplex with coefficients in a module from the cochain complexes defining Hochschild cohomology and Leibniz cohomology.","authors_text":"Ashis Mandal, Satyendra Kumar Mishra","cross_cats":["math.DG","math.RA","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-06-06T08:27:29Z","title":"Cohomology and deformations of Courant pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01654","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":"sha256:19d14985abffc53586e7f00c78fe29065c8e6dd20d0e4259aa3f51209ea8755f","target":"record","created_at":"2026-05-18T01:12:53Z","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":"84cf3844e2f8aa50442d6a83d9b41a47bd5c2f85192ad629808cefd8cfc49476","cross_cats_sorted":["math.DG","math.RA","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-06-06T08:27:29Z","title_canon_sha256":"e3ab12faec2a1160cfebacc784e831bff86d21b4360b66cdd23c62178d1c8754"},"schema_version":"1.0","source":{"id":"1606.01654","kind":"arxiv","version":1}},"canonical_sha256":"1bb3a1ed785416119a43dbe521be1fdb9f4a8d2a8656a9707b6e96f6cb390dcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bb3a1ed785416119a43dbe521be1fdb9f4a8d2a8656a9707b6e96f6cb390dcb","first_computed_at":"2026-05-18T01:12:53.836521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:53.836521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sBSYmKSJgUklWzODte8DA3fhJUrZToEiPo13GhtkSMC+iHJSKrYeAeGEp/ixVICBSxBMk/U5GFwjdaKvCavTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:53.836940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.01654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19d14985abffc53586e7f00c78fe29065c8e6dd20d0e4259aa3f51209ea8755f","sha256:e77594f72332ca0dba10de07c384b3adc801f7c21798a398ad032ee5ce41f0b6"],"state_sha256":"da886a68c551886d184e0eecacfc3321efdab42d92bb2d5a5da7655834fb4a58"}