{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:CRIOUPAMEZPLTPBJRXWZHYT27Z","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":"951a25e846c84e48b251c2408b3e7b82e41a4746145ef6503f8195cde01a206e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-03T00:36:54Z","title_canon_sha256":"a82a506562218cabce408db77bee99bd91189f2d9f3116190ad28511fbd01a2b"},"schema_version":"1.0","source":{"id":"0911.0464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0464","created_at":"2026-05-18T02:11:00Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0464v1","created_at":"2026-05-18T02:11:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0464","created_at":"2026-05-18T02:11:00Z"},{"alias_kind":"pith_short_12","alias_value":"CRIOUPAMEZPL","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CRIOUPAMEZPLTPBJ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CRIOUPAM","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:51f4488461752df24c3fd2b9c2957ffbcb592857c59a912b85507dd64a7d85c6","target":"graph","created_at":"2026-05-18T02:11:00Z","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":"We give an essentially equivalent formulation of the backward contracting property, defined by Juan Rivera-Letelier, in terms of expansion along the orbits of critical values, for complex polynomials of degree at least two which are at most finitely renormalizable and have only hyperbolic periodic points, as well as for all smooth interval maps with non-flat critical points.","authors_text":"Huaibin Li, Weixiao Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-03T00:36:54Z","title":"On non-uniformly hyperbolicity assumptions in one-dimensional dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0464","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:afd6ad6b9aa2044d757fed367b2b72ca0c7a09ed90bd1f7f1b5bc28f72d965a4","target":"record","created_at":"2026-05-18T02:11:00Z","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":"951a25e846c84e48b251c2408b3e7b82e41a4746145ef6503f8195cde01a206e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-11-03T00:36:54Z","title_canon_sha256":"a82a506562218cabce408db77bee99bd91189f2d9f3116190ad28511fbd01a2b"},"schema_version":"1.0","source":{"id":"0911.0464","kind":"arxiv","version":1}},"canonical_sha256":"1450ea3c0c265eb9bc298ded93e27afe791e1badcd03d9d66c934640cb670d11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1450ea3c0c265eb9bc298ded93e27afe791e1badcd03d9d66c934640cb670d11","first_computed_at":"2026-05-18T02:11:00.332183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:00.332183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"86AcpfXwwi1kC32Mq5EMgnMl6+nQrp0jd1At0BTR7mG+DnmletSavYVzg0Dud6LPQaWXMtZ5lETU0MiFIAr0DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:00.332971Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.0464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afd6ad6b9aa2044d757fed367b2b72ca0c7a09ed90bd1f7f1b5bc28f72d965a4","sha256:51f4488461752df24c3fd2b9c2957ffbcb592857c59a912b85507dd64a7d85c6"],"state_sha256":"27b63cc98b273a92f1824b7766084660d368ee5caecec55de03c77879396d855"}