{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TYZBCBBXXJNH52PGFHGTI4ARUN","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":"13adc85b8bbb87c5fbfabd5d3c2cffe5fd4e6c20603236412bbb066383faa4a5","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-30T06:30:45Z","title_canon_sha256":"301ab8eb45fb3b119891f9e1955597890ca172105b6a932156de45a5c63faa0f"},"schema_version":"1.0","source":{"id":"1512.08862","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08862","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08862v2","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08862","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"TYZBCBBXXJNH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"TYZBCBBXXJNH52PG","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"TYZBCBBX","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:a8f482ce2b4a51908e117b2c90a3202ce677ffef26e9dd0d3a02d9795d2b6477","target":"graph","created_at":"2026-05-18T00:47:29Z","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":"Let $\\nu_{\\alpha,q}$ be the probability and orthogonality measure for the $q$-Meixner-Pollaczek orthogonal polynomials, which has appeared in \\cite{BEH15} as the distribution of the $(\\alpha,q)$-Gaussian process (the Gaussian process of type B) over the $(\\alpha,q)$-Fock space (the Fock space of type B). The main purpose of this paper is to find the radial Bargmann representation of $\\nu_{\\alpha,q}$. Our main results cover not only the representation of $q$-Gaussian distribution by \\cite{LM95}, but also of $q^2$-Gaussian and symmetric free Meixner distributions on $\\mathbb R$. In addition, non","authors_text":"Marek Bo\\.zejko, Nobuhiro Asai, Takahiro Hasebe","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-30T06:30:45Z","title":"Radial Bargmann representation for the Fock space of type B"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08862","kind":"arxiv","version":2},"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":"sha256:7077ce3e3466db64533ea1174c6cd127a143a28c085e1b075c0e1f6743a725c4","target":"record","created_at":"2026-05-18T00:47:29Z","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":"13adc85b8bbb87c5fbfabd5d3c2cffe5fd4e6c20603236412bbb066383faa4a5","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-30T06:30:45Z","title_canon_sha256":"301ab8eb45fb3b119891f9e1955597890ca172105b6a932156de45a5c63faa0f"},"schema_version":"1.0","source":{"id":"1512.08862","kind":"arxiv","version":2}},"canonical_sha256":"9e32110437ba5a7ee9e629cd347011a37a488b983ce5784bd91d8e2107f4910c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e32110437ba5a7ee9e629cd347011a37a488b983ce5784bd91d8e2107f4910c","first_computed_at":"2026-05-18T00:47:29.413835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:29.413835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nDBlH7RcMGR+4j0mYYT4eoUFA2Ki9BF5rALDcmfQnmnBezUEwIbBee/zAYd/OwcnVqo/gk7eNAMtaPqhyp0KDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:29.414354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08862","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7077ce3e3466db64533ea1174c6cd127a143a28c085e1b075c0e1f6743a725c4","sha256:a8f482ce2b4a51908e117b2c90a3202ce677ffef26e9dd0d3a02d9795d2b6477"],"state_sha256":"f5206e8647e05c5188fa5eb4420d9549dc052dca3ff76b8e106033ffd31640d9"}