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Siegel polynomials with biaccessible critical point certainly exist, but in the Cremer case it is possible that biaccessible points can never exist.\n  As a corollary, we conclude that the set of biaccessible points in the Julia set of a Siegel or Cremer quadratic 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":"math/9801150","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1998-01-15T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"0cfdb57b22bbd93afa07f079ca0dc7f2b5982fc8b63fd9ceab004ed3fc365c11","abstract_canon_sha256":"e7b52d0198b39dd13930c31c956444fb2f94c6775519c9048c41d54f4007cb2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:34.362391Z","signature_b64":"agsf0HYCOYINdJ51h9up9KHJR7QZENbJ3EWqmjxnVTtK5Xd7RNxfQGuker/+HfaQAWznY+adnRgtO7u6WUIGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68591e9a021ccb988555a53d28204c65cbf0db44ce3d84fb521dd438fed205f4","last_reissued_at":"2026-05-18T01:05:34.361622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:34.361622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biaccessiblility in quadratic Julia sets II: The Siegel and Cremer cases","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Saeed Zakeri","submitted_at":"1998-01-15T00:00:00Z","abstract_excerpt":"Let $f$ be a quadratic polynomial which has an irrationally indifferent fixed point $\\alpha$. Let $z$ be a biaccessible point in the Julia set of $f$. Then:\n  1. In the Siegel case, the orbit of $z$ must eventually hit the critical point of $f$.\n  2. In the Cremer case, the orbit of $z$ must eventually hit the fixed point $\\alpha$. Siegel polynomials with biaccessible critical point certainly exist, but in the Cremer case it is possible that biaccessible points can never exist.\n  As a corollary, we conclude that the set of biaccessible points in the Julia set of a Siegel or Cremer quadratic po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9801150","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":"math/9801150","created_at":"2026-05-18T01:05:34.361738+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9801150v1","created_at":"2026-05-18T01:05:34.361738+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9801150","created_at":"2026-05-18T01:05:34.361738+00:00"},{"alias_kind":"pith_short_12","alias_value":"NBMR5GQCDTFZ","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"NBMR5GQCDTFZRBKV","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"NBMR5GQC","created_at":"2026-05-18T12:25:49.038998+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/NBMR5GQCDTFZRBKVUU6SQICMMX","json":"https://pith.science/pith/NBMR5GQCDTFZRBKVUU6SQICMMX.json","graph_json":"https://pith.science/api/pith-number/NBMR5GQCDTFZRBKVUU6SQICMMX/graph.json","events_json":"https://pith.science/api/pith-number/NBMR5GQCDTFZRBKVUU6SQICMMX/events.json","paper":"https://pith.science/paper/NBMR5GQC"},"agent_actions":{"view_html":"https://pith.science/pith/NBMR5GQCDTFZRBKVUU6SQICMMX","download_json":"https://pith.science/pith/NBMR5GQCDTFZRBKVUU6SQICMMX.json","view_paper":"https://pith.science/paper/NBMR5GQC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9801150&json=true","fetch_graph":"https://pith.science/api/pith-number/NBMR5GQCDTFZRBKVUU6SQICMMX/graph.json","fetch_events":"https://pith.science/api/pith-number/NBMR5GQCDTFZRBKVUU6SQICMMX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NBMR5GQCDTFZRBKVUU6SQICMMX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NBMR5GQCDTFZRBKVUU6SQICMMX/action/storage_attestation","attest_author":"https://pith.science/pith/NBMR5GQCDTFZRBKVUU6SQICMMX/action/author_attestation","sign_citation":"https://pith.science/pith/NBMR5GQCDTFZRBKVUU6SQICMMX/action/citation_signature","submit_replication":"https://pith.science/pith/NBMR5GQCDTFZRBKVUU6SQICMMX/action/replication_record"}},"created_at":"2026-05-18T01:05:34.361738+00:00","updated_at":"2026-05-18T01:05:34.361738+00:00"}