{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HVK7ZUWK2LYFLVAPWALPWFT5WW","short_pith_number":"pith:HVK7ZUWK","schema_version":"1.0","canonical_sha256":"3d55fcd2cad2f055d40fb016fb167db591c2692dda23b9a3cee5fe7c930b8b32","source":{"kind":"arxiv","id":"1310.8338","version":3},"attestation_state":"computed","paper":{"title":"Complex box bounds for real maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sebastian van Strien, Sofia Trejo, Trevor Clark","submitted_at":"2013-10-30T22:37:34Z","abstract_excerpt":"In this paper we prove complex bounds, also referred to as a priori bounds, for real analytic (and even C3) interval maps. This means that we associate to such a map a complex box mapping (which provides a kind of Markov structure), together with universal geometric bounds on the shape of the domains. Such bounds show that the first return maps to these domains are well-controlled, and consequently form one of the corner stones in many recent results on one-dimensional dynamics: renormalisation theory, rigidity results, density of hyperbolicity, local connectivity."},"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":"1310.8338","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-30T22:37:34Z","cross_cats_sorted":[],"title_canon_sha256":"d2b9f8d755c722810fe49f5132bdb80caedb6ed53a64932cff546cae88acbe4d","abstract_canon_sha256":"cf1cf9d9894d43bb5e1cf0a06e72f6e20ec8d571e3a40385ef4a9b1ca1922166"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:21.340901Z","signature_b64":"vr4t3oidMl8HbIIv7y+xIG7m9vYKQ8CyOx4D5XbJwKLCSqsdg46N9awKyyLfiaf1bAwFN9kRcx43QOagCsTyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d55fcd2cad2f055d40fb016fb167db591c2692dda23b9a3cee5fe7c930b8b32","last_reissued_at":"2026-05-18T00:53:21.340100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:21.340100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complex box bounds for real maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sebastian van Strien, Sofia Trejo, Trevor Clark","submitted_at":"2013-10-30T22:37:34Z","abstract_excerpt":"In this paper we prove complex bounds, also referred to as a priori bounds, for real analytic (and even C3) interval maps. This means that we associate to such a map a complex box mapping (which provides a kind of Markov structure), together with universal geometric bounds on the shape of the domains. Such bounds show that the first return maps to these domains are well-controlled, and consequently form one of the corner stones in many recent results on one-dimensional dynamics: renormalisation theory, rigidity results, density of hyperbolicity, local connectivity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8338","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":"1310.8338","created_at":"2026-05-18T00:53:21.340219+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.8338v3","created_at":"2026-05-18T00:53:21.340219+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8338","created_at":"2026-05-18T00:53:21.340219+00:00"},{"alias_kind":"pith_short_12","alias_value":"HVK7ZUWK2LYF","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HVK7ZUWK2LYFLVAP","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HVK7ZUWK","created_at":"2026-05-18T12:27:46.883200+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/HVK7ZUWK2LYFLVAPWALPWFT5WW","json":"https://pith.science/pith/HVK7ZUWK2LYFLVAPWALPWFT5WW.json","graph_json":"https://pith.science/api/pith-number/HVK7ZUWK2LYFLVAPWALPWFT5WW/graph.json","events_json":"https://pith.science/api/pith-number/HVK7ZUWK2LYFLVAPWALPWFT5WW/events.json","paper":"https://pith.science/paper/HVK7ZUWK"},"agent_actions":{"view_html":"https://pith.science/pith/HVK7ZUWK2LYFLVAPWALPWFT5WW","download_json":"https://pith.science/pith/HVK7ZUWK2LYFLVAPWALPWFT5WW.json","view_paper":"https://pith.science/paper/HVK7ZUWK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.8338&json=true","fetch_graph":"https://pith.science/api/pith-number/HVK7ZUWK2LYFLVAPWALPWFT5WW/graph.json","fetch_events":"https://pith.science/api/pith-number/HVK7ZUWK2LYFLVAPWALPWFT5WW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HVK7ZUWK2LYFLVAPWALPWFT5WW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HVK7ZUWK2LYFLVAPWALPWFT5WW/action/storage_attestation","attest_author":"https://pith.science/pith/HVK7ZUWK2LYFLVAPWALPWFT5WW/action/author_attestation","sign_citation":"https://pith.science/pith/HVK7ZUWK2LYFLVAPWALPWFT5WW/action/citation_signature","submit_replication":"https://pith.science/pith/HVK7ZUWK2LYFLVAPWALPWFT5WW/action/replication_record"}},"created_at":"2026-05-18T00:53:21.340219+00:00","updated_at":"2026-05-18T00:53:21.340219+00:00"}