{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:RD6DCTTNPNX2WP7JPGCYVSTWBN","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":"3eb43bc96c77393f732b45c828226a0ca959b0c16886618a4ebd6df3142ca447","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.SG","submitted_at":"2003-12-19T15:03:12Z","title_canon_sha256":"226271be4c349068aaacd1e157306528bef75fdf42ef5007b68ace583c212ec3"},"schema_version":"1.0","source":{"id":"math/0312380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0312380","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0312380v1","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312380","created_at":"2026-05-18T01:38:28Z"},{"alias_kind":"pith_short_12","alias_value":"RD6DCTTNPNX2","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"RD6DCTTNPNX2WP7J","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"RD6DCTTN","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:2d66a8df976119179411af52d8a39effeecab903d6b193999d2df62c482f6b19","target":"graph","created_at":"2026-05-18T01:38:28Z","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":"The multiplicative structure of the trivial symplectic groupoid over $\\mathbb R^d$ associated to the zero Poisson structure can be expressed in terms of a generating function. We address the problem of deforming such a generating function in the direction of a non-trivial Poisson structure so that the multiplication remains associative. We prove that such a deformation is unique under some reasonable conditions and we give the explicit formula for it. This formula turns out to be the semi-classical approximation of Kontsevich's deformation formula. For the case of a linear Poisson structure, t","authors_text":"Alberto S. Cattaneo, Benoit Dherin, Giovanni Felder","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"2003-12-19T15:03:12Z","title":"Formal symplectic groupoid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312380","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":"sha256:13631a89599a02eabc19e3fd2c3b42e55b4236b29cf20b56fb634e3828408a67","target":"record","created_at":"2026-05-18T01:38:28Z","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":"3eb43bc96c77393f732b45c828226a0ca959b0c16886618a4ebd6df3142ca447","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.SG","submitted_at":"2003-12-19T15:03:12Z","title_canon_sha256":"226271be4c349068aaacd1e157306528bef75fdf42ef5007b68ace583c212ec3"},"schema_version":"1.0","source":{"id":"math/0312380","kind":"arxiv","version":1}},"canonical_sha256":"88fc314e6d7b6fab3fe979858aca760b4d62892cefc31995d43dcd4ce669c5f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88fc314e6d7b6fab3fe979858aca760b4d62892cefc31995d43dcd4ce669c5f9","first_computed_at":"2026-05-18T01:38:28.653686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:28.653686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lNYwpBnpFcfpVbyFulxO67P3S2BADUAj8J5+8fx3TjUd/mf+Gmh3eKTPj7QBVOZ/L6xctn+n/sTk6MzpUZfFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:28.654480Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0312380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13631a89599a02eabc19e3fd2c3b42e55b4236b29cf20b56fb634e3828408a67","sha256:2d66a8df976119179411af52d8a39effeecab903d6b193999d2df62c482f6b19"],"state_sha256":"68d4f86401878f215f8e885cd2c7a969664de07a5a5cb673e421268613565fa8"}