{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:T2AFHCFLI2W7RWJ5K34PWPSZTX","short_pith_number":"pith:T2AFHCFL","schema_version":"1.0","canonical_sha256":"9e805388ab46adf8d93d56f8fb3e599de75a69a888a339b2e07a73eca934ae51","source":{"kind":"arxiv","id":"1312.4184","version":2},"attestation_state":"computed","paper":{"title":"Hyperbolicity of renormalization of circle maps with a break-type singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Konstantin Khanin, Michael Yampolsky","submitted_at":"2013-12-15T19:55:12Z","abstract_excerpt":"We study the renormalization operator of circle homeomorphisms with a break point and show that it possesses a hyperbolic horseshoe attractor."},"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":"1312.4184","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-15T19:55:12Z","cross_cats_sorted":[],"title_canon_sha256":"be88d64c14c6ec19d595184a00a9fdfe5830e4245be01d7dad8e55f8b7907680","abstract_canon_sha256":"c5570a7309ff2525ec947c1d406030074c59b60be87447f0f78778e66c0cb55f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:07.629169Z","signature_b64":"bSdfgmcDAXOrjGLi6kksGZkyqSn3+WCkYjTgjlWRA6UJZGkW0cPHK6B1VgAAaIxYFebhPuD8L8TUz5JNsNLSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e805388ab46adf8d93d56f8fb3e599de75a69a888a339b2e07a73eca934ae51","last_reissued_at":"2026-05-18T02:53:07.628423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:07.628423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hyperbolicity of renormalization of circle maps with a break-type singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Konstantin Khanin, Michael Yampolsky","submitted_at":"2013-12-15T19:55:12Z","abstract_excerpt":"We study the renormalization operator of circle homeomorphisms with a break point and show that it possesses a hyperbolic horseshoe attractor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4184","kind":"arxiv","version":2},"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":"1312.4184","created_at":"2026-05-18T02:53:07.628561+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.4184v2","created_at":"2026-05-18T02:53:07.628561+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4184","created_at":"2026-05-18T02:53:07.628561+00:00"},{"alias_kind":"pith_short_12","alias_value":"T2AFHCFLI2W7","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"T2AFHCFLI2W7RWJ5","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"T2AFHCFL","created_at":"2026-05-18T12:27:59.945178+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/T2AFHCFLI2W7RWJ5K34PWPSZTX","json":"https://pith.science/pith/T2AFHCFLI2W7RWJ5K34PWPSZTX.json","graph_json":"https://pith.science/api/pith-number/T2AFHCFLI2W7RWJ5K34PWPSZTX/graph.json","events_json":"https://pith.science/api/pith-number/T2AFHCFLI2W7RWJ5K34PWPSZTX/events.json","paper":"https://pith.science/paper/T2AFHCFL"},"agent_actions":{"view_html":"https://pith.science/pith/T2AFHCFLI2W7RWJ5K34PWPSZTX","download_json":"https://pith.science/pith/T2AFHCFLI2W7RWJ5K34PWPSZTX.json","view_paper":"https://pith.science/paper/T2AFHCFL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.4184&json=true","fetch_graph":"https://pith.science/api/pith-number/T2AFHCFLI2W7RWJ5K34PWPSZTX/graph.json","fetch_events":"https://pith.science/api/pith-number/T2AFHCFLI2W7RWJ5K34PWPSZTX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T2AFHCFLI2W7RWJ5K34PWPSZTX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T2AFHCFLI2W7RWJ5K34PWPSZTX/action/storage_attestation","attest_author":"https://pith.science/pith/T2AFHCFLI2W7RWJ5K34PWPSZTX/action/author_attestation","sign_citation":"https://pith.science/pith/T2AFHCFLI2W7RWJ5K34PWPSZTX/action/citation_signature","submit_replication":"https://pith.science/pith/T2AFHCFLI2W7RWJ5K34PWPSZTX/action/replication_record"}},"created_at":"2026-05-18T02:53:07.628561+00:00","updated_at":"2026-05-18T02:53:07.628561+00:00"}