{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:7YC6YKA3H35ACDTU54ZFKEMWIV","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":"6769c57ea1d51deceb3e0dabbcc61d741f5603032c3874ed2594cb70594dda9e","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-01-26T21:19:57Z","title_canon_sha256":"4f1d9056c64ad77cac02d1a458da8efb72fe292fb434a2ad320b12b123c2ea9b"},"schema_version":"1.0","source":{"id":"0801.4099","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.4099","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"0801.4099v2","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.4099","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"7YC6YKA3H35A","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"7YC6YKA3H35ACDTU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"7YC6YKA3","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:a57ceb1a2f2064d122a1720a1729ed691187c367e30a10d5cca6d7ddfd16c526","target":"graph","created_at":"2026-05-18T03:08:15Z","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 Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space T of the cotangent bundle of Q and hence on the standard symplectic Poisson algebra of smooth functions on T. The Poisson algebra of G-invariant functions on T yields a Poisson structure on the space T/G of G-orbits. We relate this Poisson algebra with extensions of Lie-Rinehart algebras and derive an explicit formula for this Poisson structure in terms of differentials. We then show, for the particular case where the G-action on Q is principal, how an explicit description of","authors_text":"Johannes Huebschmann, Matthew Perlmutter, Tudor S. Ratiu","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-01-26T21:19:57Z","title":"Extensions of Lie-Rinehart algebras and cotangent bundle reduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.4099","kind":"arxiv","version":2},"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":"sha256:02b6d52893329b87a712dd3ecaf858241531cea1d43aab581485065d9e2c12e9","target":"record","created_at":"2026-05-18T03:08:15Z","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":"6769c57ea1d51deceb3e0dabbcc61d741f5603032c3874ed2594cb70594dda9e","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-01-26T21:19:57Z","title_canon_sha256":"4f1d9056c64ad77cac02d1a458da8efb72fe292fb434a2ad320b12b123c2ea9b"},"schema_version":"1.0","source":{"id":"0801.4099","kind":"arxiv","version":2}},"canonical_sha256":"fe05ec281b3efa010e74ef32551196454564622a3579b0d0c9388388d618b342","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe05ec281b3efa010e74ef32551196454564622a3579b0d0c9388388d618b342","first_computed_at":"2026-05-18T03:08:15.128025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:15.128025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+3IKgFFF36fJlBr5b9DfPc1t5oRLRcPTczM36CTcG0Dwazu3U9F9s3HrbKbxvaBMaozOJD+TayrOv3AaPl5QDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:15.128713Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.4099","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02b6d52893329b87a712dd3ecaf858241531cea1d43aab581485065d9e2c12e9","sha256:a57ceb1a2f2064d122a1720a1729ed691187c367e30a10d5cca6d7ddfd16c526"],"state_sha256":"34509915631b4b5de0808e04c63aa50550b59e76ac8befe68ed5c3dc6151b40f"}