{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:PVKVOADMT4VADXVOQGVTIYCHN6","short_pith_number":"pith:PVKVOADM","canonical_record":{"source":{"id":"math/0203136","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2002-03-14T17:02:52Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1bd60ec625d3b414f5fb141fd1ef46ae229333be7986aa27bfc3d9c924f8285e","abstract_canon_sha256":"31d9eb47469460931f4b2c11feea54218a7b26b9985acb88cba8fb8518a4a1b4"},"schema_version":"1.0"},"canonical_sha256":"7d5557006c9f2a01deae81ab3460476faa4c0102b8c1667b0257cf3ea508cca1","source":{"kind":"arxiv","id":"math/0203136","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0203136","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"arxiv_version","alias_value":"math/0203136v3","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0203136","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"pith_short_12","alias_value":"PVKVOADMT4VA","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"PVKVOADMT4VADXVO","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"PVKVOADM","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:PVKVOADMT4VADXVOQGVTIYCHN6","target":"record","payload":{"canonical_record":{"source":{"id":"math/0203136","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2002-03-14T17:02:52Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"1bd60ec625d3b414f5fb141fd1ef46ae229333be7986aa27bfc3d9c924f8285e","abstract_canon_sha256":"31d9eb47469460931f4b2c11feea54218a7b26b9985acb88cba8fb8518a4a1b4"},"schema_version":"1.0"},"canonical_sha256":"7d5557006c9f2a01deae81ab3460476faa4c0102b8c1667b0257cf3ea508cca1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:13.195718Z","signature_b64":"DAqvsByd7dqqcv3NPsFzTPKtCrp8IU49NqrROG9HzmR6skSYCgx5aHf9pfUS9k6wXMe9QkIRWf01QLRcIPPSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d5557006c9f2a01deae81ab3460476faa4c0102b8c1667b0257cf3ea508cca1","last_reissued_at":"2026-05-18T03:57:13.194887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:13.194887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0203136","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":"2026-05-18T03:57:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7KGrO4Rv17H8CykUvcTL9HmLDH1pZFdm8rWjHlz9W2+m87zYZ5hSuZfYOAEYPRhB6FxUBjtf4Bj5lpGhnPP3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:51:31.631098Z"},"content_sha256":"2cfda76d4720332328becbbd871af771d58e275b50d3d9eea7266a3b78c60cce","schema_version":"1.0","event_id":"sha256:2cfda76d4720332328becbbd871af771d58e275b50d3d9eea7266a3b78c60cce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:PVKVOADMT4VADXVOQGVTIYCHN6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Askey-Wilson Type Functions, With Bound States","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.QA","authors_text":"Luc Haine, Plamen Iliev","submitted_at":"2002-03-14T17:02:52Z","abstract_excerpt":"The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful symmetry property. It essentially means that the geometric and the spectral parameters are interchangeable in these functions. We call the resulting functions the Askey-Wilson functions. Then, we show that by adding bound states (with arbitrary weights) at specific points outside of the continuous spectrum of some instances of the Askey-Wilson diffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0203136","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":"2026-05-18T03:57:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDzQzzB3IE/nyeRikJQ+I6VvFKVS6/Y+5rdh6L9CWZNeKYj6N+FvspSDwFJOvjXG015I81QoT85VEv9UbeSgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T07:51:31.631467Z"},"content_sha256":"dff51844b6f75574fe8f479f325f0f1a55710b72d47a7c5120784dd5dabfcbe2","schema_version":"1.0","event_id":"sha256:dff51844b6f75574fe8f479f325f0f1a55710b72d47a7c5120784dd5dabfcbe2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVKVOADMT4VADXVOQGVTIYCHN6/bundle.json","state_url":"https://pith.science/pith/PVKVOADMT4VADXVOQGVTIYCHN6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVKVOADMT4VADXVOQGVTIYCHN6/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":"2026-06-23T07:51:31Z","links":{"resolver":"https://pith.science/pith/PVKVOADMT4VADXVOQGVTIYCHN6","bundle":"https://pith.science/pith/PVKVOADMT4VADXVOQGVTIYCHN6/bundle.json","state":"https://pith.science/pith/PVKVOADMT4VADXVOQGVTIYCHN6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVKVOADMT4VADXVOQGVTIYCHN6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:PVKVOADMT4VADXVOQGVTIYCHN6","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":"31d9eb47469460931f4b2c11feea54218a7b26b9985acb88cba8fb8518a4a1b4","cross_cats_sorted":["math.CA"],"license":"","primary_cat":"math.QA","submitted_at":"2002-03-14T17:02:52Z","title_canon_sha256":"1bd60ec625d3b414f5fb141fd1ef46ae229333be7986aa27bfc3d9c924f8285e"},"schema_version":"1.0","source":{"id":"math/0203136","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0203136","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"arxiv_version","alias_value":"math/0203136v3","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0203136","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"pith_short_12","alias_value":"PVKVOADMT4VA","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"PVKVOADMT4VADXVO","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"PVKVOADM","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:dff51844b6f75574fe8f479f325f0f1a55710b72d47a7c5120784dd5dabfcbe2","target":"graph","created_at":"2026-05-18T03:57:13Z","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":"The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful symmetry property. It essentially means that the geometric and the spectral parameters are interchangeable in these functions. We call the resulting functions the Askey-Wilson functions. Then, we show that by adding bound states (with arbitrary weights) at specific points outside of the continuous spectrum of some instances of the Askey-Wilson diffe","authors_text":"Luc Haine, Plamen Iliev","cross_cats":["math.CA"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2002-03-14T17:02:52Z","title":"Askey-Wilson Type Functions, With Bound States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0203136","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":"sha256:2cfda76d4720332328becbbd871af771d58e275b50d3d9eea7266a3b78c60cce","target":"record","created_at":"2026-05-18T03:57:13Z","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":"31d9eb47469460931f4b2c11feea54218a7b26b9985acb88cba8fb8518a4a1b4","cross_cats_sorted":["math.CA"],"license":"","primary_cat":"math.QA","submitted_at":"2002-03-14T17:02:52Z","title_canon_sha256":"1bd60ec625d3b414f5fb141fd1ef46ae229333be7986aa27bfc3d9c924f8285e"},"schema_version":"1.0","source":{"id":"math/0203136","kind":"arxiv","version":3}},"canonical_sha256":"7d5557006c9f2a01deae81ab3460476faa4c0102b8c1667b0257cf3ea508cca1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d5557006c9f2a01deae81ab3460476faa4c0102b8c1667b0257cf3ea508cca1","first_computed_at":"2026-05-18T03:57:13.194887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:13.194887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DAqvsByd7dqqcv3NPsFzTPKtCrp8IU49NqrROG9HzmR6skSYCgx5aHf9pfUS9k6wXMe9QkIRWf01QLRcIPPSCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:13.195718Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0203136","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cfda76d4720332328becbbd871af771d58e275b50d3d9eea7266a3b78c60cce","sha256:dff51844b6f75574fe8f479f325f0f1a55710b72d47a7c5120784dd5dabfcbe2"],"state_sha256":"75e66e974c975d6fa4a373ed78f5bbd0223e66f0a559c1fdf0a12c1acbed0eed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ydHeJGtHwWnrnzw9bZaySVApM99H/UUapsEU5LgC/cqJT6iM2gdwaPxbMr+2GFGzIeEGeEcsPsLww9bCye+DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T07:51:31.633418Z","bundle_sha256":"a09a7ae206798eb5aa913eecfa2ec311694b6d84e9565d474810d2dd050b8245"}}