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We prove that for every positive measure $\\mu$ there always exists a sequence of orthogonal polynomials with respect to $\\mu$ such that all the zeros of the polynomial $q_n$ above are real and simple for $n\\ge n_0$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.11956","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2025-05-17T11:07:07Z","cross_cats_sorted":[],"title_canon_sha256":"df7596bb7d8ed8f0576c470e72b8c0d12f0707cb9797b8aa4c0d8b2d7784a5f9","abstract_canon_sha256":"18817da0ee87799013fe5fe46961e2b2006f2191acf988bf047f2d5a04bae575"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:04:55.369372Z","signature_b64":"7Dg5usWD0I8qM1/7QfNkb96xgiOHJq1E3dAdcd+AmlpB77qew1eyKSAvMRTWgNDOBNW9VRrrn47cNiEbz6xbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1323d30f1cddbaf72c4d08b5df57c754cf214f014d3973d2c0b8b523a3302e99","last_reissued_at":"2026-07-05T11:04:55.368960Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:04:55.368960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zeros of linear combinations of orthogonal polynomials","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Antonio J. 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