{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:47PMZWKZVPF2V7N7UIISFH5EL3","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":"e6ec7920de6d4b0cb3a7ccf6e61bd1c95a3e78916c6712b028381a4465f601ca","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2025-08-11T16:38:52Z","title_canon_sha256":"81a870e76e85a1f37759160c550367d385e83827ba107b9e858a0a19ac8b9d8b"},"schema_version":"1.0","source":{"id":"2508.08162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.08162","created_at":"2026-07-05T11:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"2508.08162v1","created_at":"2026-07-05T11:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.08162","created_at":"2026-07-05T11:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"47PMZWKZVPF2","created_at":"2026-07-05T11:52:09Z"},{"alias_kind":"pith_short_16","alias_value":"47PMZWKZVPF2V7N7","created_at":"2026-07-05T11:52:09Z"},{"alias_kind":"pith_short_8","alias_value":"47PMZWKZ","created_at":"2026-07-05T11:52:09Z"}],"graph_snapshots":[{"event_id":"sha256:094c0727dd8799eda921e607272bb6206263b162a3b8f0268e4794ff6356e25b","target":"graph","created_at":"2026-07-05T11:52:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.08162/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we exhaustively explore the terminating basic hypergeometric representations and transformations of the $q$ and $q^{-1}$-symmetric subfamilies of the Askey--Wilson polynomials. These subfamilies are obtained by repeatedly setting one of the free parameters (not $q$) equal to zero until no parameters are left. These subfamilies (and their $q^{-1}$ counterparts) are the continuous dual $q$-Hahn, Al-Salam--Chihara, continuous big $q$-Hermite, and the continuous $q$-Hermite polynomials. From the terminating basic hypergeometric representations of these polynomials, and due to symm","authors_text":"Howard S. Cohl, Linus Ge, Roberto S. Costas-Santos","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2025-08-11T16:38:52Z","title":"Terminating representations, transformations and summations for the $q$ and $q^{-1}$-symmetric subfamilies of the Askey--Wilson polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.08162","kind":"arxiv","version":1},"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:aa321106e216ba46103627700b3ddc0c4d7d92960eaf0a0a103100db3795e764","target":"record","created_at":"2026-07-05T11:52:09Z","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":"e6ec7920de6d4b0cb3a7ccf6e61bd1c95a3e78916c6712b028381a4465f601ca","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2025-08-11T16:38:52Z","title_canon_sha256":"81a870e76e85a1f37759160c550367d385e83827ba107b9e858a0a19ac8b9d8b"},"schema_version":"1.0","source":{"id":"2508.08162","kind":"arxiv","version":1}},"canonical_sha256":"e7deccd959abcbaafdbfa211229fa45efa2eb2f8e22d01c8d70bdeb174f12a75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7deccd959abcbaafdbfa211229fa45efa2eb2f8e22d01c8d70bdeb174f12a75","first_computed_at":"2026-07-05T11:52:09.215263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:52:09.215263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UAVeN3qaZaAIUdwWoS2F28nD/3MYN7zWUGQHqCYKR+uVp5NZ/tigHyrQbEC/ctNrgZnTAuihDHgVUR+evfl9AA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:52:09.215708Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.08162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa321106e216ba46103627700b3ddc0c4d7d92960eaf0a0a103100db3795e764","sha256:094c0727dd8799eda921e607272bb6206263b162a3b8f0268e4794ff6356e25b"],"state_sha256":"dff504eec06c832cd7d64a4e9c8f065249052ca2b9b101b569e8790ba876c5f8"}