{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZFV3BKJ2YD6CE4XGD7N22JLWRI","short_pith_number":"pith:ZFV3BKJ2","schema_version":"1.0","canonical_sha256":"c96bb0a93ac0fc2272e61fdbad25768a154df3da8e634df57787f9f98f6b25c2","source":{"kind":"arxiv","id":"1504.08278","version":1},"attestation_state":"computed","paper":{"title":"Chebyshev polynomials on generalized Julia sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"G\\\"okalp Alpan","submitted_at":"2015-04-30T15:45:30Z","abstract_excerpt":"Let $(f_n)_{n=1}^\\infty$ be a sequence of nonlinear polynomials satisfying some mild conditions. Furthermore, let $F_m(z)=(f_m\\circ f_{m-1}\\ldots \\circ f_1)(z)$ and $\\rho_m$ be the leading coefficient for $F_m$. It is shown that on the Julia set $J_{(f_n)}$, the Chebyshev polynomial of the degree deg${F_m}$ is of the form $F_m(z)/\\rho_m-\\tau_m$ for all $m\\in\\mathbb{N}$ where $\\tau_m\\in\\mathbb{C}$. This generalizes the result obtained for autonomous Julia sets."},"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":"1504.08278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-30T15:45:30Z","cross_cats_sorted":[],"title_canon_sha256":"f4db768a8a0f586799d2b9fa355a75d233163236e16663626569202c640d48f9","abstract_canon_sha256":"49306931a38ef57324930e7f63f85d3e37cf20112516905115487874a14376c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:41.102702Z","signature_b64":"nJ7vUW5PczqJsjnxAH9HXxD8+FwDLilegZW4cwXSXT+bBNAUXII1HEc24yPaDIF8P4Jhxb6ll1TDgG57047VBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c96bb0a93ac0fc2272e61fdbad25768a154df3da8e634df57787f9f98f6b25c2","last_reissued_at":"2026-05-18T01:06:41.102064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:41.102064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chebyshev polynomials on generalized Julia sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"G\\\"okalp Alpan","submitted_at":"2015-04-30T15:45:30Z","abstract_excerpt":"Let $(f_n)_{n=1}^\\infty$ be a sequence of nonlinear polynomials satisfying some mild conditions. Furthermore, let $F_m(z)=(f_m\\circ f_{m-1}\\ldots \\circ f_1)(z)$ and $\\rho_m$ be the leading coefficient for $F_m$. It is shown that on the Julia set $J_{(f_n)}$, the Chebyshev polynomial of the degree deg${F_m}$ is of the form $F_m(z)/\\rho_m-\\tau_m$ for all $m\\in\\mathbb{N}$ where $\\tau_m\\in\\mathbb{C}$. This generalizes the result obtained for autonomous Julia sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08278","kind":"arxiv","version":1},"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":"1504.08278","created_at":"2026-05-18T01:06:41.102162+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.08278v1","created_at":"2026-05-18T01:06:41.102162+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08278","created_at":"2026-05-18T01:06:41.102162+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZFV3BKJ2YD6C","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZFV3BKJ2YD6CE4XG","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZFV3BKJ2","created_at":"2026-05-18T12:29:52.810259+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/ZFV3BKJ2YD6CE4XGD7N22JLWRI","json":"https://pith.science/pith/ZFV3BKJ2YD6CE4XGD7N22JLWRI.json","graph_json":"https://pith.science/api/pith-number/ZFV3BKJ2YD6CE4XGD7N22JLWRI/graph.json","events_json":"https://pith.science/api/pith-number/ZFV3BKJ2YD6CE4XGD7N22JLWRI/events.json","paper":"https://pith.science/paper/ZFV3BKJ2"},"agent_actions":{"view_html":"https://pith.science/pith/ZFV3BKJ2YD6CE4XGD7N22JLWRI","download_json":"https://pith.science/pith/ZFV3BKJ2YD6CE4XGD7N22JLWRI.json","view_paper":"https://pith.science/paper/ZFV3BKJ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.08278&json=true","fetch_graph":"https://pith.science/api/pith-number/ZFV3BKJ2YD6CE4XGD7N22JLWRI/graph.json","fetch_events":"https://pith.science/api/pith-number/ZFV3BKJ2YD6CE4XGD7N22JLWRI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZFV3BKJ2YD6CE4XGD7N22JLWRI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZFV3BKJ2YD6CE4XGD7N22JLWRI/action/storage_attestation","attest_author":"https://pith.science/pith/ZFV3BKJ2YD6CE4XGD7N22JLWRI/action/author_attestation","sign_citation":"https://pith.science/pith/ZFV3BKJ2YD6CE4XGD7N22JLWRI/action/citation_signature","submit_replication":"https://pith.science/pith/ZFV3BKJ2YD6CE4XGD7N22JLWRI/action/replication_record"}},"created_at":"2026-05-18T01:06:41.102162+00:00","updated_at":"2026-05-18T01:06:41.102162+00:00"}