{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YBZBOFS34NTDFJYRAZ3HIZACCQ","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":"1ad67f401f12ba250f71961e44e606b208f59b68593fdbcb7137fb4270719091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-09T07:09:38Z","title_canon_sha256":"9825e6ef54f566e67c4875f3e336612f692a38f8d90f28e359a0fad8fb2d089f"},"schema_version":"1.0","source":{"id":"1510.02579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02579","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02579v1","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02579","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"YBZBOFS34NTD","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YBZBOFS34NTDFJYR","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YBZBOFS3","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:a3f72c5bbf129509b912d90e4aa93a1f2bae8e8ce1d60473175fb302e30bae0d","target":"graph","created_at":"2026-05-18T01:30:42Z","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":"Using Casorati determinants of Hahn polynomials $(h_n^{\\alpha,\\beta,N})_n$, we construct for each pair $\\F=(F_1,F_2)$ of finite sets of positive integers polynomials $h_n^{\\alpha,\\beta,N;\\F}$, $n\\in \\sigma _\\F$, which are eigenfunctions of a second order difference operator, where $\\sigma _\\F$ is certain set of nonnegative integers, $\\sigma _\\F \\varsubsetneq \\NN$. When $N\\in \\NN$ and $\\alpha$, $\\beta$, $N$ and $\\F$ satisfy a suitable admissibility condition, we prove that the polynomials $h_n^{\\alpha,\\beta,N;\\F}$ are also orthogonal and complete with respect to a positive measure (exceptional ","authors_text":"Antonio J. Dur\\'an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-09T07:09:38Z","title":"Exceptional Hahn and Jacobi orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02579","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:ef3256bc0b9f0f7ab48e5c8bde785020074cdbea0bb386dd45182a132d2fa537","target":"record","created_at":"2026-05-18T01:30:42Z","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":"1ad67f401f12ba250f71961e44e606b208f59b68593fdbcb7137fb4270719091","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-09T07:09:38Z","title_canon_sha256":"9825e6ef54f566e67c4875f3e336612f692a38f8d90f28e359a0fad8fb2d089f"},"schema_version":"1.0","source":{"id":"1510.02579","kind":"arxiv","version":1}},"canonical_sha256":"c07217165be36632a7110676746402141ca9b7baa733dfd2e9b613c10609f3fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c07217165be36632a7110676746402141ca9b7baa733dfd2e9b613c10609f3fc","first_computed_at":"2026-05-18T01:30:42.033127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:42.033127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CRub/AQD2ATwt8WZLyKtzhN/xni1+hmxdax5I9DugE2vWntQOf41a8N0qNaiB6nqUfn+k8TW3OkSiFHuH5f7DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:42.033809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.02579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef3256bc0b9f0f7ab48e5c8bde785020074cdbea0bb386dd45182a132d2fa537","sha256:a3f72c5bbf129509b912d90e4aa93a1f2bae8e8ce1d60473175fb302e30bae0d"],"state_sha256":"a8cf21492c3dc40510567545d4883532a87783311cadd0452bae7f8ed9cbb88e"}