{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EGHGNAOYIM7LOMNLLO5KEEWP3D","short_pith_number":"pith:EGHGNAOY","schema_version":"1.0","canonical_sha256":"218e6681d8433eb731ab5bbaa212cfd8f465bb924fe8e9e8cf43595b61eb8473","source":{"kind":"arxiv","id":"1712.04250","version":5},"attestation_state":"computed","paper":{"title":"On three dimensional multivariate version of q-Normal distribution and probabilistic interpretations of Askey--Wilson, Al-Salam--Chihara and q-ultraspherical polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pawe{\\l} J. Szab{\\l}owski","submitted_at":"2017-12-12T11:48:35Z","abstract_excerpt":"We study properties of compactly supported, 4 parameter \\newline $(\\rho _{12},\\rho _{23},\\rho _{13},q)\\in (-1,1)^{\\times 4}$ family of continuous type 3 dimensional distributions, that have the property that for $q\\rightarrow 1^{-}$ this family tends to some 3 dimensional Normal distribution. For $q=0$ we deal with 3 dimensional generalization of Kesten--McKay distribution. In a very special case when $\\rho _{12}\\rho _{13}\\rho _{23}=q$ all one dimensional marginals are identical, semicircle distributions. We find both all marginal as well as all conditional distributions. Moreover, we find als"},"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":"1712.04250","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-12T11:48:35Z","cross_cats_sorted":[],"title_canon_sha256":"52780ffb57b6168bea72870f1e6389d8914fcac3f9592a41c84d75cb2c7480f0","abstract_canon_sha256":"958b728126c55fb0b2ab627b71fe52e88b366c18d356903dc8913813d613ebb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:16.793805Z","signature_b64":"lasunpPHLLk+EK2viAMwsuNRfGSSH/UBh8Un5D1sIX8Yd9uu3wWOWMOnPYH0ujHimNYIfxm2xq8pLfON3dPSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"218e6681d8433eb731ab5bbaa212cfd8f465bb924fe8e9e8cf43595b61eb8473","last_reissued_at":"2026-05-17T23:54:16.792997Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:16.792997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On three dimensional multivariate version of q-Normal distribution and probabilistic interpretations of Askey--Wilson, Al-Salam--Chihara and q-ultraspherical polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pawe{\\l} J. Szab{\\l}owski","submitted_at":"2017-12-12T11:48:35Z","abstract_excerpt":"We study properties of compactly supported, 4 parameter \\newline $(\\rho _{12},\\rho _{23},\\rho _{13},q)\\in (-1,1)^{\\times 4}$ family of continuous type 3 dimensional distributions, that have the property that for $q\\rightarrow 1^{-}$ this family tends to some 3 dimensional Normal distribution. For $q=0$ we deal with 3 dimensional generalization of Kesten--McKay distribution. In a very special case when $\\rho _{12}\\rho _{13}\\rho _{23}=q$ all one dimensional marginals are identical, semicircle distributions. We find both all marginal as well as all conditional distributions. Moreover, we find als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04250","kind":"arxiv","version":5},"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":"1712.04250","created_at":"2026-05-17T23:54:16.793133+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.04250v5","created_at":"2026-05-17T23:54:16.793133+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04250","created_at":"2026-05-17T23:54:16.793133+00:00"},{"alias_kind":"pith_short_12","alias_value":"EGHGNAOYIM7L","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EGHGNAOYIM7LOMNL","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EGHGNAOY","created_at":"2026-05-18T12:31:12.930513+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/EGHGNAOYIM7LOMNLLO5KEEWP3D","json":"https://pith.science/pith/EGHGNAOYIM7LOMNLLO5KEEWP3D.json","graph_json":"https://pith.science/api/pith-number/EGHGNAOYIM7LOMNLLO5KEEWP3D/graph.json","events_json":"https://pith.science/api/pith-number/EGHGNAOYIM7LOMNLLO5KEEWP3D/events.json","paper":"https://pith.science/paper/EGHGNAOY"},"agent_actions":{"view_html":"https://pith.science/pith/EGHGNAOYIM7LOMNLLO5KEEWP3D","download_json":"https://pith.science/pith/EGHGNAOYIM7LOMNLLO5KEEWP3D.json","view_paper":"https://pith.science/paper/EGHGNAOY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.04250&json=true","fetch_graph":"https://pith.science/api/pith-number/EGHGNAOYIM7LOMNLLO5KEEWP3D/graph.json","fetch_events":"https://pith.science/api/pith-number/EGHGNAOYIM7LOMNLLO5KEEWP3D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EGHGNAOYIM7LOMNLLO5KEEWP3D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EGHGNAOYIM7LOMNLLO5KEEWP3D/action/storage_attestation","attest_author":"https://pith.science/pith/EGHGNAOYIM7LOMNLLO5KEEWP3D/action/author_attestation","sign_citation":"https://pith.science/pith/EGHGNAOYIM7LOMNLLO5KEEWP3D/action/citation_signature","submit_replication":"https://pith.science/pith/EGHGNAOYIM7LOMNLLO5KEEWP3D/action/replication_record"}},"created_at":"2026-05-17T23:54:16.793133+00:00","updated_at":"2026-05-17T23:54:16.793133+00:00"}