{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:45C7XZY72YYCYCV4AAANRK5E4O","short_pith_number":"pith:45C7XZY7","schema_version":"1.0","canonical_sha256":"e745fbe71fd6302c0abc0000d8aba4e3a294329930656f2362d3726fe99d1959","source":{"kind":"arxiv","id":"math/0507244","version":1},"attestation_state":"computed","paper":{"title":"Fedosov's formal symplectic groupoids and contravariant connections","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.QA","authors_text":"Alexander V. Karabegov","submitted_at":"2005-07-12T19:12:40Z","abstract_excerpt":"Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kaehler-Poisson manifolds this construction provides, in particular, the formal symplectic groupoids with separation of variables. We show that the dual of a semisimple Lie algebra does not admit torsion-free Poisson contravariant connections."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0507244","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2005-07-12T19:12:40Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"581b4bd7e6b2953a9bd0df8da0b2f9d74949927360948ee0505d2eae5641ff38","abstract_canon_sha256":"3f3add0018564fc0a3ad6905595af1629113f65bd9dc4a682fbef5d69663c969"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:24.927541Z","signature_b64":"jpGqonF7a4grfSQm7BVnY14wugYO54QTopef7Ug7l5M+KIg8AFFvC+5qDCOFNu0s78w8f5Wln83LG7zxJ0jsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e745fbe71fd6302c0abc0000d8aba4e3a294329930656f2362d3726fe99d1959","last_reissued_at":"2026-05-18T01:38:24.926822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:24.926822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fedosov's formal symplectic groupoids and contravariant connections","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.QA","authors_text":"Alexander V. Karabegov","submitted_at":"2005-07-12T19:12:40Z","abstract_excerpt":"Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kaehler-Poisson manifolds this construction provides, in particular, the formal symplectic groupoids with separation of variables. We show that the dual of a semisimple Lie algebra does not admit torsion-free Poisson contravariant connections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507244","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0507244","created_at":"2026-05-18T01:38:24.926940+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0507244v1","created_at":"2026-05-18T01:38:24.926940+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0507244","created_at":"2026-05-18T01:38:24.926940+00:00"},{"alias_kind":"pith_short_12","alias_value":"45C7XZY72YYC","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"45C7XZY72YYCYCV4","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"45C7XZY7","created_at":"2026-05-18T12:25:52.687210+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/45C7XZY72YYCYCV4AAANRK5E4O","json":"https://pith.science/pith/45C7XZY72YYCYCV4AAANRK5E4O.json","graph_json":"https://pith.science/api/pith-number/45C7XZY72YYCYCV4AAANRK5E4O/graph.json","events_json":"https://pith.science/api/pith-number/45C7XZY72YYCYCV4AAANRK5E4O/events.json","paper":"https://pith.science/paper/45C7XZY7"},"agent_actions":{"view_html":"https://pith.science/pith/45C7XZY72YYCYCV4AAANRK5E4O","download_json":"https://pith.science/pith/45C7XZY72YYCYCV4AAANRK5E4O.json","view_paper":"https://pith.science/paper/45C7XZY7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0507244&json=true","fetch_graph":"https://pith.science/api/pith-number/45C7XZY72YYCYCV4AAANRK5E4O/graph.json","fetch_events":"https://pith.science/api/pith-number/45C7XZY72YYCYCV4AAANRK5E4O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/45C7XZY72YYCYCV4AAANRK5E4O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/45C7XZY72YYCYCV4AAANRK5E4O/action/storage_attestation","attest_author":"https://pith.science/pith/45C7XZY72YYCYCV4AAANRK5E4O/action/author_attestation","sign_citation":"https://pith.science/pith/45C7XZY72YYCYCV4AAANRK5E4O/action/citation_signature","submit_replication":"https://pith.science/pith/45C7XZY72YYCYCV4AAANRK5E4O/action/replication_record"}},"created_at":"2026-05-18T01:38:24.926940+00:00","updated_at":"2026-05-18T01:38:24.926940+00:00"}