{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WDUEB5ILQWDEQNQ5QSPJH5GMOS","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":"d229d72f5c54810836d2f6113fc8a6b8322fc211f788c342d1d056164445fea5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-17T23:44:58Z","title_canon_sha256":"6793b43e6b00b9c15c5466dd3f0595fe6ca9161c6924c4f24c2cb63a5bee6076"},"schema_version":"1.0","source":{"id":"1907.07814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07814","created_at":"2026-05-17T23:40:16Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07814v1","created_at":"2026-05-17T23:40:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07814","created_at":"2026-05-17T23:40:16Z"},{"alias_kind":"pith_short_12","alias_value":"WDUEB5ILQWDE","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WDUEB5ILQWDEQNQ5","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WDUEB5IL","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:00bc2c321f64e75a78282740db03eec89bbb4ecff2fa7283af610881371329e6","target":"graph","created_at":"2026-05-17T23:40:16Z","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":"Classical Gon\\v{c}arov polynomials arose in numerical analysis as a basis for the solutions of the Gon\\v{c}arov interpolation problem. These polynomials provide a natural algebraic tool in the enumerative theory of parking functions. By replacing the differentiation operator with a delta operator and using the theory of finite operator calculus, Lorentz, Tringali and Yan introduced the sequence of generalized Gon\\v{c}arov polynomials associated to a pair $(\\Delta, Z)$ of a delta operator $\\Delta$ and an interpolation grid $Z$. Generalized Gon\\v{c}arov polynomials share many nice algebraic prop","authors_text":"Ayomikun Adeniran, Catherine Yan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-17T23:44:58Z","title":"Gon\\v{c}arov Polynomials in Partition Lattices and Exponential Families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07814","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:b690170aa902be59e1e5105888ce63850316aa1babf7dc5e88456b0d7725e93f","target":"record","created_at":"2026-05-17T23:40:16Z","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":"d229d72f5c54810836d2f6113fc8a6b8322fc211f788c342d1d056164445fea5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-17T23:44:58Z","title_canon_sha256":"6793b43e6b00b9c15c5466dd3f0595fe6ca9161c6924c4f24c2cb63a5bee6076"},"schema_version":"1.0","source":{"id":"1907.07814","kind":"arxiv","version":1}},"canonical_sha256":"b0e840f50b858648361d849e93f4cc7491d435b2a32d473d89ae98bbeeeeb5b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0e840f50b858648361d849e93f4cc7491d435b2a32d473d89ae98bbeeeeb5b1","first_computed_at":"2026-05-17T23:40:16.204920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:16.204920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5lz2yhZgKpkC1sNcnNGR7pInQYC8Ib4N+ii3PBvYUik7Eain9v5D/fXPuCXmZJHT1v24gT+YbttsIdV8hQwNBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:16.205672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.07814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b690170aa902be59e1e5105888ce63850316aa1babf7dc5e88456b0d7725e93f","sha256:00bc2c321f64e75a78282740db03eec89bbb4ecff2fa7283af610881371329e6"],"state_sha256":"3ee488ebd18d451ce996487e3ab255077b92340f0f89799d82022966f0257aeb"}