{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HFLPQZQD5TGYY6RQZM5NZRBERY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"81bf6ff5d507395546db943284a4c3f2e207e9f0194b18eba48643368c438df9","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-01-06T20:08:33Z","title_canon_sha256":"fa35af4aa188bb6fcb7cf30d2f38216402c4bc7bee8bbf001e4153583009d9f9"},"schema_version":"1.0","source":{"id":"1001.0953","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0953","created_at":"2026-05-18T01:22:52Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0953v3","created_at":"2026-05-18T01:22:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0953","created_at":"2026-05-18T01:22:52Z"},{"alias_kind":"pith_short_12","alias_value":"HFLPQZQD5TGY","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HFLPQZQD5TGYY6RQ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HFLPQZQD","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:bff699c4fd7f402aa5243888906ba51b5183252f17343b533d10e534e58fbf87","target":"graph","created_at":"2026-05-18T01:22:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $P$ be a polynomial of degree $d$ with Julia set $J_P$. Let $\\widetilde N$ be the number of non-repelling cycles of $P$. By the famous Fatou-Shishikura inequality $\\widetilde N\\le d-1$. The goal of the paper is to improve this bound. The new count includes \\emph{wandering collections of non-precritical branch continua}, i.e., collections of continua or points $Q_i\\subset J_P$ \\emph{all} of whose images are pairwise disjoint, contain no critical points, and contain the limit sets of $\\mathrm{eval}(Q_i)\\ge 3$ external rays. Also, we relate individual cycles, which are either non-repelling or","authors_text":"Alexander Blokh, Dierk Schleicher, Doug Childers, Genadi Levin, Lex Oversteegen","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-01-06T20:08:33Z","title":"An Extended Fatou-Shishikura inequality and wandering branch continua for polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0953","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bc091d4b381f686ea958dcf209e45dcf3b617ecaba5c53723ec77cef75af3889","target":"record","created_at":"2026-05-18T01:22:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"81bf6ff5d507395546db943284a4c3f2e207e9f0194b18eba48643368c438df9","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-01-06T20:08:33Z","title_canon_sha256":"fa35af4aa188bb6fcb7cf30d2f38216402c4bc7bee8bbf001e4153583009d9f9"},"schema_version":"1.0","source":{"id":"1001.0953","kind":"arxiv","version":3}},"canonical_sha256":"3956f86603eccd8c7a30cb3adcc4248e2cc5b5d96434e85374741b4145c14e04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3956f86603eccd8c7a30cb3adcc4248e2cc5b5d96434e85374741b4145c14e04","first_computed_at":"2026-05-18T01:22:52.720167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:52.720167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YdtNjZ+C6wYnCHFofr75xnE8j86dssYDuaKMFeopb0hLzidFJAuXw62hnljod3TyIP2q+NYoKYm+oxLJ+7XlAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:52.720625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.0953","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc091d4b381f686ea958dcf209e45dcf3b617ecaba5c53723ec77cef75af3889","sha256:bff699c4fd7f402aa5243888906ba51b5183252f17343b533d10e534e58fbf87"],"state_sha256":"30d2c99055525e7db1163c8fa4789d825e6f9aa5ea14dd70ded350a2dee25924"}