{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NR3ADCTKQHG5CAYX2WKQIXB5PI","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":"d329b36954587747803db08f90c928125f1171fed1da401dd83bcaa4950118f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-04T12:08:07Z","title_canon_sha256":"f22b267491c2ab36669387cdfee2a6bce9189ee1dc631abc77e4b8e36f51d5c5"},"schema_version":"1.0","source":{"id":"1309.0995","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0995","created_at":"2026-05-18T01:29:29Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0995v1","created_at":"2026-05-18T01:29:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0995","created_at":"2026-05-18T01:29:29Z"},{"alias_kind":"pith_short_12","alias_value":"NR3ADCTKQHG5","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NR3ADCTKQHG5CAYX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NR3ADCTK","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:c954dfe5da6da37a9f88ca83c72f25f15babd9ecf524065e2aecb27868d36cd4","target":"graph","created_at":"2026-05-18T01:29:29Z","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":"The objective of this manuscript is to study directly the Favard type theorem associated with the three term recurrence formula % \\[ R_{n+1}(z) = \\big[(1+ic_{n+1})z+(1-ic_{n+1})\\big] R_{n}(z) - 4 d_{n+1} z R_{n-1}(z), \\quad n \\geq 1, \\] % with $R_{0}(z) =1$ and $R_{1}(z) = (1+ic_{1})z+(1-ic_{1})$, where $\\{c_n\\}_{n=1}^{\\infty}$ is a real sequence and $\\{d_n\\}_{n=1}^{\\infty}$ is a positive chain sequence. We establish that there exists an unique nontrivial probability measure $\\mu$ on the unit circle for which $\\{R_n(z) - 2(1-m_n)R_{n-1}(z)\\}$ gives the sequence of orthogonal polynomials. Here,","authors_text":"A. Sri Ranga, Daniel Veronese, Kenier Castillo, Marisa Costa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-04T12:08:07Z","title":"A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0995","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:a76cc15c3e1985da7496b3842901204e39403ea439f3eb071fb63116d6190657","target":"record","created_at":"2026-05-18T01:29:29Z","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":"d329b36954587747803db08f90c928125f1171fed1da401dd83bcaa4950118f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-04T12:08:07Z","title_canon_sha256":"f22b267491c2ab36669387cdfee2a6bce9189ee1dc631abc77e4b8e36f51d5c5"},"schema_version":"1.0","source":{"id":"1309.0995","kind":"arxiv","version":1}},"canonical_sha256":"6c76018a6a81cdd10317d595045c3d7a0b3cc6da9388a39125f39572ec5cf5f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c76018a6a81cdd10317d595045c3d7a0b3cc6da9388a39125f39572ec5cf5f5","first_computed_at":"2026-05-18T01:29:29.878960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:29.878960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hY348SbqLPdOy9gsWwpp3eLB88dMCHqJ0WvQEiAmIQqKjLzOwuBsDaFgv+cpb7PivtbDa37U4XBK9JR3aL3dAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:29.879428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0995","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a76cc15c3e1985da7496b3842901204e39403ea439f3eb071fb63116d6190657","sha256:c954dfe5da6da37a9f88ca83c72f25f15babd9ecf524065e2aecb27868d36cd4"],"state_sha256":"0d574fc991ce2f5c9d62b6a672090d4cea85eaa4b71f4c6331a8e37220e5cc8f"}