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Let us further assume that $(F_n)_{n=1}^\\infty$ is a sequence of orthogonal polynomials for $\\mu$ where $(f_n)_{n=1}^\\infty$ is a sequence of nonlinear polynomials and $F_n:=f_n\\circ\\dots\\circ f_1$ for all $n\\in\\mathbb{N}$. We prove that if there is an $s_0\\in\\mathbb{N}$ such that $0$ is a root of $f_n^\\prime$ for each $n>s_0$ then the distance between any two zeros of an orthogonal polynomial for $\\mu$ of a given degree greater than $1$ has a lower bound in terms of the distance between the set of critical po"},"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":"1509.07391","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-09-24T14:39:19Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5dd0448fafdacbbedeb476d7048a9f247ced0bf5e225bd14b1ce64b6d6ee1842","abstract_canon_sha256":"8144e279e2f6a48d1c0bf9391ecaf7e814a3d5d37f49e8358d4ba2aac9c2c4da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:27.208251Z","signature_b64":"+CYjAS8AEv3UqeAAzaQ9cNUZrQHzhylX5ZFx8PeDlwP2sAfdU5sPPb6nXS3j7LzYJroVlgrPYPqqx5UQCly9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9736ad88f8132540db8cb5baecc52e6cdb7fed7fdde9db6a17ca0df77b8fe06c","last_reissued_at":"2026-05-18T01:11:27.207526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:27.207526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spacing properties of the zeros of orthogonal polynomials on Cantor sets via a sequence of polynomial mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.SP","authors_text":"G\\\"okalp Alpan","submitted_at":"2015-09-24T14:39:19Z","abstract_excerpt":"Let $\\mu$ be a probability measure with an infinite compact support on $\\mathbb{R}$. Let us further assume that $(F_n)_{n=1}^\\infty$ is a sequence of orthogonal polynomials for $\\mu$ where $(f_n)_{n=1}^\\infty$ is a sequence of nonlinear polynomials and $F_n:=f_n\\circ\\dots\\circ f_1$ for all $n\\in\\mathbb{N}$. We prove that if there is an $s_0\\in\\mathbb{N}$ such that $0$ is a root of $f_n^\\prime$ for each $n>s_0$ then the distance between any two zeros of an orthogonal polynomial for $\\mu$ of a given degree greater than $1$ has a lower bound in terms of the distance between the set of critical po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07391","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.07391","created_at":"2026-05-18T01:11:27.207637+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07391v2","created_at":"2026-05-18T01:11:27.207637+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07391","created_at":"2026-05-18T01:11:27.207637+00:00"},{"alias_kind":"pith_short_12","alias_value":"S43K3CHYCMSU","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"S43K3CHYCMSUBW4M","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"S43K3CHY","created_at":"2026-05-18T12:29:39.896362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S43K3CHYCMSUBW4MWW5OZRJONT","json":"https://pith.science/pith/S43K3CHYCMSUBW4MWW5OZRJONT.json","graph_json":"https://pith.science/api/pith-number/S43K3CHYCMSUBW4MWW5OZRJONT/graph.json","events_json":"https://pith.science/api/pith-number/S43K3CHYCMSUBW4MWW5OZRJONT/events.json","paper":"https://pith.science/paper/S43K3CHY"},"agent_actions":{"view_html":"https://pith.science/pith/S43K3CHYCMSUBW4MWW5OZRJONT","download_json":"https://pith.science/pith/S43K3CHYCMSUBW4MWW5OZRJONT.json","view_paper":"https://pith.science/paper/S43K3CHY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07391&json=true","fetch_graph":"https://pith.science/api/pith-number/S43K3CHYCMSUBW4MWW5OZRJONT/graph.json","fetch_events":"https://pith.science/api/pith-number/S43K3CHYCMSUBW4MWW5OZRJONT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S43K3CHYCMSUBW4MWW5OZRJONT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S43K3CHYCMSUBW4MWW5OZRJONT/action/storage_attestation","attest_author":"https://pith.science/pith/S43K3CHYCMSUBW4MWW5OZRJONT/action/author_attestation","sign_citation":"https://pith.science/pith/S43K3CHYCMSUBW4MWW5OZRJONT/action/citation_signature","submit_replication":"https://pith.science/pith/S43K3CHYCMSUBW4MWW5OZRJONT/action/replication_record"}},"created_at":"2026-05-18T01:11:27.207637+00:00","updated_at":"2026-05-18T01:11:27.207637+00:00"}