{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:T4RBNO6HOCSPH4J5663O47VDSA","short_pith_number":"pith:T4RBNO6H","schema_version":"1.0","canonical_sha256":"9f2216bbc770a4f3f13df7b6ee7ea3903d36f615aff4c16ea1592c2c54ef915a","source":{"kind":"arxiv","id":"1305.5799","version":3},"attestation_state":"computed","paper":{"title":"Quadratic-like dynamics of cubic polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexander Blokh, Lex Oversteegen, Ross Ptacek, Vladlen Timorin","submitted_at":"2013-05-24T17:03:21Z","abstract_excerpt":"A small perturbation of a quadratic polynomial with a non-repelling fixed point gives a polynomial with an attracting fixed point and a Jordan curve Julia set, on which the perturbed polynomial acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions."},"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":"1305.5799","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-24T17:03:21Z","cross_cats_sorted":[],"title_canon_sha256":"4bb7837e24383fb80d8d5c2ab23a9f653233e2479fdad5fe4ae7e22fce677908","abstract_canon_sha256":"2c6a8e30a3a55bd4c1a8935ae8ea4e25e7c7e360405faafe8420d75df5f1bf01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:40.867247Z","signature_b64":"NJvJv5ODY9/xsnsY6vzrMuLvzk5H7vfQU9SioS81KEw0rpat+o+uzc1boe6HY0AbF7IGKQPDNPYkyFhUKjXRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f2216bbc770a4f3f13df7b6ee7ea3903d36f615aff4c16ea1592c2c54ef915a","last_reissued_at":"2026-05-18T01:21:40.866787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:40.866787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quadratic-like dynamics of cubic polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexander Blokh, Lex Oversteegen, Ross Ptacek, Vladlen Timorin","submitted_at":"2013-05-24T17:03:21Z","abstract_excerpt":"A small perturbation of a quadratic polynomial with a non-repelling fixed point gives a polynomial with an attracting fixed point and a Jordan curve Julia set, on which the perturbed polynomial acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5799","kind":"arxiv","version":3},"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":"1305.5799","created_at":"2026-05-18T01:21:40.866852+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.5799v3","created_at":"2026-05-18T01:21:40.866852+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5799","created_at":"2026-05-18T01:21:40.866852+00:00"},{"alias_kind":"pith_short_12","alias_value":"T4RBNO6HOCSP","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"T4RBNO6HOCSPH4J5","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"T4RBNO6H","created_at":"2026-05-18T12:27:59.945178+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/T4RBNO6HOCSPH4J5663O47VDSA","json":"https://pith.science/pith/T4RBNO6HOCSPH4J5663O47VDSA.json","graph_json":"https://pith.science/api/pith-number/T4RBNO6HOCSPH4J5663O47VDSA/graph.json","events_json":"https://pith.science/api/pith-number/T4RBNO6HOCSPH4J5663O47VDSA/events.json","paper":"https://pith.science/paper/T4RBNO6H"},"agent_actions":{"view_html":"https://pith.science/pith/T4RBNO6HOCSPH4J5663O47VDSA","download_json":"https://pith.science/pith/T4RBNO6HOCSPH4J5663O47VDSA.json","view_paper":"https://pith.science/paper/T4RBNO6H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.5799&json=true","fetch_graph":"https://pith.science/api/pith-number/T4RBNO6HOCSPH4J5663O47VDSA/graph.json","fetch_events":"https://pith.science/api/pith-number/T4RBNO6HOCSPH4J5663O47VDSA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T4RBNO6HOCSPH4J5663O47VDSA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T4RBNO6HOCSPH4J5663O47VDSA/action/storage_attestation","attest_author":"https://pith.science/pith/T4RBNO6HOCSPH4J5663O47VDSA/action/author_attestation","sign_citation":"https://pith.science/pith/T4RBNO6HOCSPH4J5663O47VDSA/action/citation_signature","submit_replication":"https://pith.science/pith/T4RBNO6HOCSPH4J5663O47VDSA/action/replication_record"}},"created_at":"2026-05-18T01:21:40.866852+00:00","updated_at":"2026-05-18T01:21:40.866852+00:00"}