{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:Z7T57L7VIAYKTQCAWSNRQTCU6W","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":"0b1ba846c8770e148d45310fac53ded778af37a6a465f58503bec5dbf5451548","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.DS","submitted_at":"2008-01-30T12:36:09Z","title_canon_sha256":"bc59cb92c168f973fc28acb14d30a55290fd7de4e06aaf356f966cc1b653e6fc"},"schema_version":"1.0","source":{"id":"0801.4662","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.4662","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"arxiv_version","alias_value":"0801.4662v1","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.4662","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"pith_short_12","alias_value":"Z7T57L7VIAYK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"Z7T57L7VIAYKTQCA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"Z7T57L7V","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:1ea6868312eb439e4fcac29accefdfa40cf2c4a5d0712d1da9cc1c71b65ab3ff","target":"graph","created_at":"2026-05-18T02:58:11Z","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":"Hubbard trees are invariant trees connecting the points of the critical orbits of postcritically finite polynomials. Douady and Hubbard \\cite{Orsay} introduced these trees and showed that they encode the essential information of Julia sets in a combinatorial way. The itinerary of the critical orbit within the Hubbard tree is encoded by a (pre)periodic sequence on $\\{\\0,\\1\\}$ called \\emph{kneading sequence}.\n  We prove that the kneading sequence completely encodes the Hubbard tree and its dynamics, and we show how to reconstruct the tree and in particular its branch points (together with their ","authors_text":"Dierk Schleicher, Henk Bruin","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2008-01-30T12:36:09Z","title":"Admissibility of kneading sequences and structure of Hubbard trees for quadratic polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.4662","kind":"arxiv","version":1},"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":"sha256:3471844e36935b5ccecab17fd5cad949a5af7ee85a152a5eb16975ea58c0b6b8","target":"record","created_at":"2026-05-18T02:58:11Z","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":"0b1ba846c8770e148d45310fac53ded778af37a6a465f58503bec5dbf5451548","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.DS","submitted_at":"2008-01-30T12:36:09Z","title_canon_sha256":"bc59cb92c168f973fc28acb14d30a55290fd7de4e06aaf356f966cc1b653e6fc"},"schema_version":"1.0","source":{"id":"0801.4662","kind":"arxiv","version":1}},"canonical_sha256":"cfe7dfaff54030a9c040b49b184c54f5a18f9561931f71835760bf163570642f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfe7dfaff54030a9c040b49b184c54f5a18f9561931f71835760bf163570642f","first_computed_at":"2026-05-18T02:58:11.874818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:11.874818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+BLVR9qLUrEEcY2MA8sUi3+wNBWF90GY2Wbznhz6ZrLm1NschYo+rsFAq3atnEwzRWiIDv9jAbLyYQlsvnBgAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:11.875765Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.4662","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3471844e36935b5ccecab17fd5cad949a5af7ee85a152a5eb16975ea58c0b6b8","sha256:1ea6868312eb439e4fcac29accefdfa40cf2c4a5d0712d1da9cc1c71b65ab3ff"],"state_sha256":"036286f900e19d9af17ef316ca81ee041514f88e8dfb2156fdb2733114740cf7"}