{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EGHGNAOYIM7LOMNLLO5KEEWP3D","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":"958b728126c55fb0b2ab627b71fe52e88b366c18d356903dc8913813d613ebb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-12T11:48:35Z","title_canon_sha256":"52780ffb57b6168bea72870f1e6389d8914fcac3f9592a41c84d75cb2c7480f0"},"schema_version":"1.0","source":{"id":"1712.04250","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04250","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04250v5","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04250","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"EGHGNAOYIM7L","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EGHGNAOYIM7LOMNL","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EGHGNAOY","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:f9fd5aad8d250e604db19a21c29ce61a01e4315cd5bab88e46d969ac2f4c1969","target":"graph","created_at":"2026-05-17T23:54:16Z","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":"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","authors_text":"Pawe{\\l} J. Szab{\\l}owski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-12T11:48:35Z","title":"On three dimensional multivariate version of q-Normal distribution and probabilistic interpretations of Askey--Wilson, Al-Salam--Chihara and q-ultraspherical polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04250","kind":"arxiv","version":5},"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":"sha256:28157b3f4750baa038c7e9db60097068157959b5941ce8a50af17f8a45029593","target":"record","created_at":"2026-05-17T23:54:16Z","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":"958b728126c55fb0b2ab627b71fe52e88b366c18d356903dc8913813d613ebb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-12T11:48:35Z","title_canon_sha256":"52780ffb57b6168bea72870f1e6389d8914fcac3f9592a41c84d75cb2c7480f0"},"schema_version":"1.0","source":{"id":"1712.04250","kind":"arxiv","version":5}},"canonical_sha256":"218e6681d8433eb731ab5bbaa212cfd8f465bb924fe8e9e8cf43595b61eb8473","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"218e6681d8433eb731ab5bbaa212cfd8f465bb924fe8e9e8cf43595b61eb8473","first_computed_at":"2026-05-17T23:54:16.792997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:16.792997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lasunpPHLLk+EK2viAMwsuNRfGSSH/UBh8Un5D1sIX8Yd9uu3wWOWMOnPYH0ujHimNYIfxm2xq8pLfON3dPSCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:16.793805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04250","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28157b3f4750baa038c7e9db60097068157959b5941ce8a50af17f8a45029593","sha256:f9fd5aad8d250e604db19a21c29ce61a01e4315cd5bab88e46d969ac2f4c1969"],"state_sha256":"8c1c7151ae0ca66aeefeaff2432176c6ef781b467cec93b6fb02e353c4a95e17"}