{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YHZDCBWEC4RS7FCVXTHPLPIXZE","short_pith_number":"pith:YHZDCBWE","schema_version":"1.0","canonical_sha256":"c1f23106c417232f9455bccef5bd17c92ed56912dd756694ec69d156ed124bcd","source":{"kind":"arxiv","id":"1108.3024","version":4},"attestation_state":"computed","paper":{"title":"Around Poisson--Mehler summation formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Pawe{\\l} J. Szab{\\l}owski","submitted_at":"2011-08-15T15:50:20Z","abstract_excerpt":"We study polynomials in $x$ and $y$ of degree $n+m:\\allowbreak \\{Q_{m,n}(x,y|t,q)\\}_{n,m\\geq 0}$ that appeared recently in the following identity: $\\gamma_{m,n}(x,y|t,q) \\allowbreak =\\allowbreak \\gamma_{0,0}(x,y|t,q) \\allowbreak Q_{m,n}(x,y|t,q) $ where $\\gamma_{m,n}(x,y|t,q) \\allowbreak =\\allowbreak \\sum_{i\\geq 0}\\frac{t^{i}}{[i]_{q}}H_{i+n}(x|q) H_{m+i}(y|q)$, $\\allowbreak $ $\\{H_{n}(x|q)}_{n\\geq -1}$ are the so-called $q-$% Hermite polynomials (qH). In particular we show that the spaces $span\\{Q_{i,n-i}(x,y|t,q) :i=0,...,n\\}_{n\\geq 0}$ are orthogonal with respect to a certain measure (two-d"},"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":"1108.3024","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-08-15T15:50:20Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f742d6ff0dc691be6a11c5e72edcb1cfcdcd2c1199c22549da96f1c38d4a54f1","abstract_canon_sha256":"6363288056d091fa54a505a416e4b841c34e6c565c559fd1e48ab9e8ec64167d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:06.441742Z","signature_b64":"14ya5IohHI6ORrUnC0WZ/p7Afz4bJMJ08WHgN4fX0lKzfbf8cM4Vy7LGOGDwKJl/fZfo+infJJZiZSfg8co/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1f23106c417232f9455bccef5bd17c92ed56912dd756694ec69d156ed124bcd","last_reissued_at":"2026-05-18T03:28:06.440900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:06.440900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Around Poisson--Mehler summation formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Pawe{\\l} J. Szab{\\l}owski","submitted_at":"2011-08-15T15:50:20Z","abstract_excerpt":"We study polynomials in $x$ and $y$ of degree $n+m:\\allowbreak \\{Q_{m,n}(x,y|t,q)\\}_{n,m\\geq 0}$ that appeared recently in the following identity: $\\gamma_{m,n}(x,y|t,q) \\allowbreak =\\allowbreak \\gamma_{0,0}(x,y|t,q) \\allowbreak Q_{m,n}(x,y|t,q) $ where $\\gamma_{m,n}(x,y|t,q) \\allowbreak =\\allowbreak \\sum_{i\\geq 0}\\frac{t^{i}}{[i]_{q}}H_{i+n}(x|q) H_{m+i}(y|q)$, $\\allowbreak $ $\\{H_{n}(x|q)}_{n\\geq -1}$ are the so-called $q-$% Hermite polynomials (qH). In particular we show that the spaces $span\\{Q_{i,n-i}(x,y|t,q) :i=0,...,n\\}_{n\\geq 0}$ are orthogonal with respect to a certain measure (two-d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3024","kind":"arxiv","version":4},"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":"1108.3024","created_at":"2026-05-18T03:28:06.441027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.3024v4","created_at":"2026-05-18T03:28:06.441027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3024","created_at":"2026-05-18T03:28:06.441027+00:00"},{"alias_kind":"pith_short_12","alias_value":"YHZDCBWEC4RS","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YHZDCBWEC4RS7FCV","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YHZDCBWE","created_at":"2026-05-18T12:26:47.523578+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/YHZDCBWEC4RS7FCVXTHPLPIXZE","json":"https://pith.science/pith/YHZDCBWEC4RS7FCVXTHPLPIXZE.json","graph_json":"https://pith.science/api/pith-number/YHZDCBWEC4RS7FCVXTHPLPIXZE/graph.json","events_json":"https://pith.science/api/pith-number/YHZDCBWEC4RS7FCVXTHPLPIXZE/events.json","paper":"https://pith.science/paper/YHZDCBWE"},"agent_actions":{"view_html":"https://pith.science/pith/YHZDCBWEC4RS7FCVXTHPLPIXZE","download_json":"https://pith.science/pith/YHZDCBWEC4RS7FCVXTHPLPIXZE.json","view_paper":"https://pith.science/paper/YHZDCBWE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.3024&json=true","fetch_graph":"https://pith.science/api/pith-number/YHZDCBWEC4RS7FCVXTHPLPIXZE/graph.json","fetch_events":"https://pith.science/api/pith-number/YHZDCBWEC4RS7FCVXTHPLPIXZE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YHZDCBWEC4RS7FCVXTHPLPIXZE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YHZDCBWEC4RS7FCVXTHPLPIXZE/action/storage_attestation","attest_author":"https://pith.science/pith/YHZDCBWEC4RS7FCVXTHPLPIXZE/action/author_attestation","sign_citation":"https://pith.science/pith/YHZDCBWEC4RS7FCVXTHPLPIXZE/action/citation_signature","submit_replication":"https://pith.science/pith/YHZDCBWEC4RS7FCVXTHPLPIXZE/action/replication_record"}},"created_at":"2026-05-18T03:28:06.441027+00:00","updated_at":"2026-05-18T03:28:06.441027+00:00"}