{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D5JWP47GCNO4FIQY4OMKCIDHG3","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":"dec08862277cfd1f725e29ba51c5b71432f0616e14721e5b31a9a4b28bd055f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-07T09:50:19Z","title_canon_sha256":"18dd84191ff7fd379e5b8269d6e4c57163c39cf2dbfac20d9082e4fb0ccfc3a3"},"schema_version":"1.0","source":{"id":"1312.2076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2076","created_at":"2026-05-18T03:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2076v1","created_at":"2026-05-18T03:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2076","created_at":"2026-05-18T03:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"D5JWP47GCNO4","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D5JWP47GCNO4FIQY","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D5JWP47G","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:fbd714edb3d349771ca1d4a66a2ce5d9f276b66e54056bbdf8c5806e5a802ea3","target":"graph","created_at":"2026-05-18T03:05:17Z","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":"Let $G$ be a connected Lie group and $\\mathfrak{g}$ its Lie algebra. We denote by $\\nabla^0$ the torsion free bi-invariant linear connection on $G$ given by $\\nabla^0_XY=\\frac12[X,Y],$ for any left invariant vector fields $X,Y$. A Poisson structure on $\\mathfrak{g}$ is a commutative and associative product on $\\mathfrak{g}$ for which $\\mathrm{ad}_u$ is a derivation, for any $u\\in\\mathfrak{g}$.\n  A torsion free bi-invariant linear connections on $G$ which have the same curvature as $\\nabla^0$ is called special. We show that there is a bijection between the space of special connections on $G$ an","authors_text":"Mohamed Boucetta, Sa\\\"id Benayadi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-07T09:50:19Z","title":"Special bi-invariant linear connections on Lie groups and finite dimensional Poisson structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2076","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:a0d51a2e321ffd705c483a67336773bbe9be368cce15f83005e1323f58c951a0","target":"record","created_at":"2026-05-18T03:05:17Z","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":"dec08862277cfd1f725e29ba51c5b71432f0616e14721e5b31a9a4b28bd055f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-07T09:50:19Z","title_canon_sha256":"18dd84191ff7fd379e5b8269d6e4c57163c39cf2dbfac20d9082e4fb0ccfc3a3"},"schema_version":"1.0","source":{"id":"1312.2076","kind":"arxiv","version":1}},"canonical_sha256":"1f5367f3e6135dc2a218e398a1206736eb3a877206c3c244374e5e8fe4352c6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f5367f3e6135dc2a218e398a1206736eb3a877206c3c244374e5e8fe4352c6b","first_computed_at":"2026-05-18T03:05:17.401184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:17.401184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1eqB9Lk6kfGAVZgd/BHCrf+mZy3ziXCKL2rF3KeLPYt6F8mmiNAAkM9FmUa8WLUQKe5ocJvqG1kDbXPIp9ECBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:17.401669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0d51a2e321ffd705c483a67336773bbe9be368cce15f83005e1323f58c951a0","sha256:fbd714edb3d349771ca1d4a66a2ce5d9f276b66e54056bbdf8c5806e5a802ea3"],"state_sha256":"294b785e08541947aeb2f08dbae0f1f89e213140a2a0b16118af56390ba19307"}