{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:A65WZGR73OYCNASNYQM3HTLHGV","short_pith_number":"pith:A65WZGR7","schema_version":"1.0","canonical_sha256":"07bb6c9a3fdbb026824dc419b3cd67354fa305c25ac9ddcc0b668d58fa1a89ce","source":{"kind":"arxiv","id":"1411.6268","version":2},"attestation_state":"computed","paper":{"title":"Infinitesimal generators for a class of polynomial processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OA"],"primary_cat":"math.PR","authors_text":"Jacek Wesolowski, Wlodzimierz Bryc","submitted_at":"2014-11-23T17:03:51Z","abstract_excerpt":"We study the infinitesimal generators of evolutions of linear mappings on the space of polynomials, which correspond to a special class of Markov processes with polynomial regressions called quadratic harnesses. We relate the infinitesimal generator to the unique solution of a certain commutation equation, and we use the commutation equation to find an explicit formula for the infinitesimal generator of free quadratic harnesses."},"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":"1411.6268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-23T17:03:51Z","cross_cats_sorted":["math.CO","math.OA"],"title_canon_sha256":"27993a790944575b6c0f3c1a266c15ea34628d875561fb449895a6ac6134b9e7","abstract_canon_sha256":"8dcb48f06fc95fd50540b86e32dc838dfd375fb86228f66835431df18020509b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:36.007281Z","signature_b64":"8HZik9uUa2yaDKUyj9Bb3sK2vB9N9AEeaePF6u2jdu5KRmZIe9dNfLzTeyImDAqPnFbBylvnvJ1Kh8BinFBMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07bb6c9a3fdbb026824dc419b3cd67354fa305c25ac9ddcc0b668d58fa1a89ce","last_reissued_at":"2026-05-18T00:50:36.006571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:36.006571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitesimal generators for a class of polynomial processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OA"],"primary_cat":"math.PR","authors_text":"Jacek Wesolowski, Wlodzimierz Bryc","submitted_at":"2014-11-23T17:03:51Z","abstract_excerpt":"We study the infinitesimal generators of evolutions of linear mappings on the space of polynomials, which correspond to a special class of Markov processes with polynomial regressions called quadratic harnesses. We relate the infinitesimal generator to the unique solution of a certain commutation equation, and we use the commutation equation to find an explicit formula for the infinitesimal generator of free quadratic harnesses."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6268","kind":"arxiv","version":2},"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":"1411.6268","created_at":"2026-05-18T00:50:36.006686+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.6268v2","created_at":"2026-05-18T00:50:36.006686+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6268","created_at":"2026-05-18T00:50:36.006686+00:00"},{"alias_kind":"pith_short_12","alias_value":"A65WZGR73OYC","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"A65WZGR73OYCNASN","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"A65WZGR7","created_at":"2026-05-18T12:28:19.803747+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/A65WZGR73OYCNASNYQM3HTLHGV","json":"https://pith.science/pith/A65WZGR73OYCNASNYQM3HTLHGV.json","graph_json":"https://pith.science/api/pith-number/A65WZGR73OYCNASNYQM3HTLHGV/graph.json","events_json":"https://pith.science/api/pith-number/A65WZGR73OYCNASNYQM3HTLHGV/events.json","paper":"https://pith.science/paper/A65WZGR7"},"agent_actions":{"view_html":"https://pith.science/pith/A65WZGR73OYCNASNYQM3HTLHGV","download_json":"https://pith.science/pith/A65WZGR73OYCNASNYQM3HTLHGV.json","view_paper":"https://pith.science/paper/A65WZGR7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.6268&json=true","fetch_graph":"https://pith.science/api/pith-number/A65WZGR73OYCNASNYQM3HTLHGV/graph.json","fetch_events":"https://pith.science/api/pith-number/A65WZGR73OYCNASNYQM3HTLHGV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A65WZGR73OYCNASNYQM3HTLHGV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A65WZGR73OYCNASNYQM3HTLHGV/action/storage_attestation","attest_author":"https://pith.science/pith/A65WZGR73OYCNASNYQM3HTLHGV/action/author_attestation","sign_citation":"https://pith.science/pith/A65WZGR73OYCNASNYQM3HTLHGV/action/citation_signature","submit_replication":"https://pith.science/pith/A65WZGR73OYCNASNYQM3HTLHGV/action/replication_record"}},"created_at":"2026-05-18T00:50:36.006686+00:00","updated_at":"2026-05-18T00:50:36.006686+00:00"}