{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UZIYTIE6YFZYJQNDBJQJTQFXWL","short_pith_number":"pith:UZIYTIE6","canonical_record":{"source":{"id":"1411.5223","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-18T00:56:32Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"79a2ff47651653278dcd330ff0b35009f0b583d9132c18de4bbd954c1e7823a8","abstract_canon_sha256":"6ea0b21be5d8e816efdde8b898e11a09960c979158b3a871b3bcee3ffbc5e32e"},"schema_version":"1.0"},"canonical_sha256":"a65189a09ec17384c1a30a6099c0b7b2deea08b51ceb0f35460d0eecccbc5993","source":{"kind":"arxiv","id":"1411.5223","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5223","created_at":"2026-05-18T01:35:01Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5223v3","created_at":"2026-05-18T01:35:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5223","created_at":"2026-05-18T01:35:01Z"},{"alias_kind":"pith_short_12","alias_value":"UZIYTIE6YFZY","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UZIYTIE6YFZYJQND","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UZIYTIE6","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UZIYTIE6YFZYJQNDBJQJTQFXWL","target":"record","payload":{"canonical_record":{"source":{"id":"1411.5223","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-18T00:56:32Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"79a2ff47651653278dcd330ff0b35009f0b583d9132c18de4bbd954c1e7823a8","abstract_canon_sha256":"6ea0b21be5d8e816efdde8b898e11a09960c979158b3a871b3bcee3ffbc5e32e"},"schema_version":"1.0"},"canonical_sha256":"a65189a09ec17384c1a30a6099c0b7b2deea08b51ceb0f35460d0eecccbc5993","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:01.721172Z","signature_b64":"IyBYWKVIiBJqbZA+Fm7uoOHBbnDje7wOxFjB3xfPbBiiLYZKWhFBMmtNT0YYPiiiQCTabqTZP+Fb2i1Mv79aAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a65189a09ec17384c1a30a6099c0b7b2deea08b51ceb0f35460d0eecccbc5993","last_reissued_at":"2026-05-18T01:35:01.720545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:01.720545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.5223","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:35:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ROJYJhT/0oIU+CLUX3hzvZ2Eh+ZAVvQZCenHjgAanAj7GxcJmS/lcJg+x/g93ey3bZrDJFzn+xbWOS7AM5AAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:13:07.554160Z"},"content_sha256":"34d05c4a82ff5987c38ef58e4aef7791f91cf7cc26f0bc7d9aef99f7cc2f6ee8","schema_version":"1.0","event_id":"sha256:34d05c4a82ff5987c38ef58e4aef7791f91cf7cc26f0bc7d9aef99f7cc2f6ee8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UZIYTIE6YFZYJQNDBJQJTQFXWL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On some 2D orthogonal q-polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.CA","authors_text":"Mourad E. H. Ismail, Ruiming Zhang","submitted_at":"2014-11-18T00:56:32Z","abstract_excerpt":"We introduce two q-analogues of the 2D-Hermite polynomials which are functions of two complex variables. We derive explicit formulas, orthogonality relations, raising and lowering operator relations, generating functions, and Rodrigues formulas for both families. We also introduce a q-2D analogue of the disk polynomials (Zernike polynomials) and derive similar formulas for them as well including evaluating certain connection coefficients. Some of the generating functions may be related to Rogers-Ramanujan type identities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5223","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:35:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"phLKNgWa3xJhytEBqv+s+YDfzi+rx5+sWLExXuRsCsZbPyOS6MeZzo1Rw2imh06yRcm9M/AYJnCE2L7GW/lDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:13:07.554581Z"},"content_sha256":"ec37d598cc642e2e05696f0cf29ad382615ffdb861e2cf5879827a135d6722ae","schema_version":"1.0","event_id":"sha256:ec37d598cc642e2e05696f0cf29ad382615ffdb861e2cf5879827a135d6722ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZIYTIE6YFZYJQNDBJQJTQFXWL/bundle.json","state_url":"https://pith.science/pith/UZIYTIE6YFZYJQNDBJQJTQFXWL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZIYTIE6YFZYJQNDBJQJTQFXWL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T22:13:07Z","links":{"resolver":"https://pith.science/pith/UZIYTIE6YFZYJQNDBJQJTQFXWL","bundle":"https://pith.science/pith/UZIYTIE6YFZYJQNDBJQJTQFXWL/bundle.json","state":"https://pith.science/pith/UZIYTIE6YFZYJQNDBJQJTQFXWL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZIYTIE6YFZYJQNDBJQJTQFXWL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UZIYTIE6YFZYJQNDBJQJTQFXWL","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":"6ea0b21be5d8e816efdde8b898e11a09960c979158b3a871b3bcee3ffbc5e32e","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-18T00:56:32Z","title_canon_sha256":"79a2ff47651653278dcd330ff0b35009f0b583d9132c18de4bbd954c1e7823a8"},"schema_version":"1.0","source":{"id":"1411.5223","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5223","created_at":"2026-05-18T01:35:01Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5223v3","created_at":"2026-05-18T01:35:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5223","created_at":"2026-05-18T01:35:01Z"},{"alias_kind":"pith_short_12","alias_value":"UZIYTIE6YFZY","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UZIYTIE6YFZYJQND","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UZIYTIE6","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:ec37d598cc642e2e05696f0cf29ad382615ffdb861e2cf5879827a135d6722ae","target":"graph","created_at":"2026-05-18T01:35:01Z","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 introduce two q-analogues of the 2D-Hermite polynomials which are functions of two complex variables. We derive explicit formulas, orthogonality relations, raising and lowering operator relations, generating functions, and Rodrigues formulas for both families. We also introduce a q-2D analogue of the disk polynomials (Zernike polynomials) and derive similar formulas for them as well including evaluating certain connection coefficients. Some of the generating functions may be related to Rogers-Ramanujan type identities.","authors_text":"Mourad E. H. Ismail, Ruiming Zhang","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-18T00:56:32Z","title":"On some 2D orthogonal q-polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5223","kind":"arxiv","version":3},"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":"sha256:34d05c4a82ff5987c38ef58e4aef7791f91cf7cc26f0bc7d9aef99f7cc2f6ee8","target":"record","created_at":"2026-05-18T01:35:01Z","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":"6ea0b21be5d8e816efdde8b898e11a09960c979158b3a871b3bcee3ffbc5e32e","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-11-18T00:56:32Z","title_canon_sha256":"79a2ff47651653278dcd330ff0b35009f0b583d9132c18de4bbd954c1e7823a8"},"schema_version":"1.0","source":{"id":"1411.5223","kind":"arxiv","version":3}},"canonical_sha256":"a65189a09ec17384c1a30a6099c0b7b2deea08b51ceb0f35460d0eecccbc5993","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a65189a09ec17384c1a30a6099c0b7b2deea08b51ceb0f35460d0eecccbc5993","first_computed_at":"2026-05-18T01:35:01.720545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:01.720545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IyBYWKVIiBJqbZA+Fm7uoOHBbnDje7wOxFjB3xfPbBiiLYZKWhFBMmtNT0YYPiiiQCTabqTZP+Fb2i1Mv79aAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:01.721172Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5223","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34d05c4a82ff5987c38ef58e4aef7791f91cf7cc26f0bc7d9aef99f7cc2f6ee8","sha256:ec37d598cc642e2e05696f0cf29ad382615ffdb861e2cf5879827a135d6722ae"],"state_sha256":"97a0e0686fbb56e2b745f3509979da3f2f9bc4392e4877bdcf1b2c1a5cf1a2cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fG+xNSaX3O86KTSOSI6DZzQr8yMopyXIexgWx6DmosXq8+hpHY2dzvYsbor8h3CbDM43V4nnysBCZh7OvFasAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:13:07.556755Z","bundle_sha256":"0ad70c78e4d69f37a5973f14fdf4a45f56e5a17cf884584b694a1e1087263300"}}