{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NOG4PA34VMDUNAPLQQVEZVREP2","short_pith_number":"pith:NOG4PA34","schema_version":"1.0","canonical_sha256":"6b8dc7837cab074681eb842a4cd6247eab732dc04bb5ee7d64c0aa1b361a7305","source":{"kind":"arxiv","id":"1506.07970","version":1},"attestation_state":"computed","paper":{"title":"Moments of q-Normal and conditional q-Normal distributions","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":"2015-06-26T07:19:56Z","abstract_excerpt":"We calculate moments and moment generating functions of two distributions: the so called $q-$Normal and the so called conditional $q-$Normal distributions. These distributions generalize both Normal ($q=1),$ Wigner ($% q=0,$ $q-$Normal) and Kesten-McKay ($q=0,$ conditional $q-$Normal) distributions. As a by product we get asymptotic properties of some expansions in modified Bessel functions."},"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":"1506.07970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-26T07:19:56Z","cross_cats_sorted":[],"title_canon_sha256":"d2b0601ed1692c5997232a50e3e4f814ae6b79898f3f6a42b3ae520fd47dc6c2","abstract_canon_sha256":"ec86881afee94e27b872ed8839a15fffcfe91ff009e7188ba9e0667e1442d074"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:43.016163Z","signature_b64":"dI71HRxhuBNRZSRIhUaUd912UrJSRGarSEnNbNqyerrva6K9x/ZCPeDHxeEZLZUVomoKftd/9iq/B34zAN5yDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b8dc7837cab074681eb842a4cd6247eab732dc04bb5ee7d64c0aa1b361a7305","last_reissued_at":"2026-05-18T01:36:43.015603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:43.015603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moments of q-Normal and conditional q-Normal distributions","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":"2015-06-26T07:19:56Z","abstract_excerpt":"We calculate moments and moment generating functions of two distributions: the so called $q-$Normal and the so called conditional $q-$Normal distributions. These distributions generalize both Normal ($q=1),$ Wigner ($% q=0,$ $q-$Normal) and Kesten-McKay ($q=0,$ conditional $q-$Normal) distributions. As a by product we get asymptotic properties of some expansions in modified Bessel functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07970","kind":"arxiv","version":1},"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":"1506.07970","created_at":"2026-05-18T01:36:43.015682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.07970v1","created_at":"2026-05-18T01:36:43.015682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07970","created_at":"2026-05-18T01:36:43.015682+00:00"},{"alias_kind":"pith_short_12","alias_value":"NOG4PA34VMDU","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NOG4PA34VMDUNAPL","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NOG4PA34","created_at":"2026-05-18T12:29:34.919912+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/NOG4PA34VMDUNAPLQQVEZVREP2","json":"https://pith.science/pith/NOG4PA34VMDUNAPLQQVEZVREP2.json","graph_json":"https://pith.science/api/pith-number/NOG4PA34VMDUNAPLQQVEZVREP2/graph.json","events_json":"https://pith.science/api/pith-number/NOG4PA34VMDUNAPLQQVEZVREP2/events.json","paper":"https://pith.science/paper/NOG4PA34"},"agent_actions":{"view_html":"https://pith.science/pith/NOG4PA34VMDUNAPLQQVEZVREP2","download_json":"https://pith.science/pith/NOG4PA34VMDUNAPLQQVEZVREP2.json","view_paper":"https://pith.science/paper/NOG4PA34","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.07970&json=true","fetch_graph":"https://pith.science/api/pith-number/NOG4PA34VMDUNAPLQQVEZVREP2/graph.json","fetch_events":"https://pith.science/api/pith-number/NOG4PA34VMDUNAPLQQVEZVREP2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NOG4PA34VMDUNAPLQQVEZVREP2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NOG4PA34VMDUNAPLQQVEZVREP2/action/storage_attestation","attest_author":"https://pith.science/pith/NOG4PA34VMDUNAPLQQVEZVREP2/action/author_attestation","sign_citation":"https://pith.science/pith/NOG4PA34VMDUNAPLQQVEZVREP2/action/citation_signature","submit_replication":"https://pith.science/pith/NOG4PA34VMDUNAPLQQVEZVREP2/action/replication_record"}},"created_at":"2026-05-18T01:36:43.015682+00:00","updated_at":"2026-05-18T01:36:43.015682+00:00"}