{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2QER4INFRVNTCUQLSWE2Q4IM2H","short_pith_number":"pith:2QER4INF","schema_version":"1.0","canonical_sha256":"d4091e21a58d5b31520b9589a8710cd1cdbab06505855c6a3c242541d6b89f73","source":{"kind":"arxiv","id":"1706.03654","version":3},"attestation_state":"computed","paper":{"title":"On the renormalizations of circle homeomorphisms with several break points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Abdumajid Begmatov, Akhtam Dzhalilov, Kleyber Cunha","submitted_at":"2017-06-12T14:21:39Z","abstract_excerpt":"Let $f$ be an orientation preserving homeomorphisms on the circle with several break points, that is, its derivative $Df$ has jump discontinuities at these points. We study Rauzy-Veech renormalizations of piecewise smooth circle homeomorphisms, by considering such maps as generalized interval exchange maps with genus one. Suppose that $Df$ is absolutely continuous on the each interval of continuity and $D\\ln{Df}\\in \\mathbb{L}_{p}$ for some $p>1$. We prove that, under certain combinatorial assumptions on $f$, renormalizations $R^{n}(f)$ are approximated by piecewise M\\\"{o}bus functions in $C^{1"},"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":"1706.03654","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-12T14:21:39Z","cross_cats_sorted":[],"title_canon_sha256":"178b518dc1ff38d62d75d915bbdf969741dcf3a583bd8ce51c8a5fed075635d2","abstract_canon_sha256":"01c9061f90b29c7e49f4ef7d19ee9e15c5b66f0ed0a5cc14428be57cd3bf5673"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:42.272023Z","signature_b64":"WtsGYbhEAYZkiw8gjIjpcLkub/Zn/u7uuMQlBTlMJm7p0lxVigr3TlGsGssemmXiF53vRWcQ0owMQd18BAaTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4091e21a58d5b31520b9589a8710cd1cdbab06505855c6a3c242541d6b89f73","last_reissued_at":"2026-05-18T00:09:42.271109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:42.271109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the renormalizations of circle homeomorphisms with several break points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Abdumajid Begmatov, Akhtam Dzhalilov, Kleyber Cunha","submitted_at":"2017-06-12T14:21:39Z","abstract_excerpt":"Let $f$ be an orientation preserving homeomorphisms on the circle with several break points, that is, its derivative $Df$ has jump discontinuities at these points. We study Rauzy-Veech renormalizations of piecewise smooth circle homeomorphisms, by considering such maps as generalized interval exchange maps with genus one. Suppose that $Df$ is absolutely continuous on the each interval of continuity and $D\\ln{Df}\\in \\mathbb{L}_{p}$ for some $p>1$. We prove that, under certain combinatorial assumptions on $f$, renormalizations $R^{n}(f)$ are approximated by piecewise M\\\"{o}bus functions in $C^{1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03654","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":"1706.03654","created_at":"2026-05-18T00:09:42.271264+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.03654v3","created_at":"2026-05-18T00:09:42.271264+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03654","created_at":"2026-05-18T00:09:42.271264+00:00"},{"alias_kind":"pith_short_12","alias_value":"2QER4INFRVNT","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2QER4INFRVNTCUQL","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2QER4INF","created_at":"2026-05-18T12:30:55.937587+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/2QER4INFRVNTCUQLSWE2Q4IM2H","json":"https://pith.science/pith/2QER4INFRVNTCUQLSWE2Q4IM2H.json","graph_json":"https://pith.science/api/pith-number/2QER4INFRVNTCUQLSWE2Q4IM2H/graph.json","events_json":"https://pith.science/api/pith-number/2QER4INFRVNTCUQLSWE2Q4IM2H/events.json","paper":"https://pith.science/paper/2QER4INF"},"agent_actions":{"view_html":"https://pith.science/pith/2QER4INFRVNTCUQLSWE2Q4IM2H","download_json":"https://pith.science/pith/2QER4INFRVNTCUQLSWE2Q4IM2H.json","view_paper":"https://pith.science/paper/2QER4INF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.03654&json=true","fetch_graph":"https://pith.science/api/pith-number/2QER4INFRVNTCUQLSWE2Q4IM2H/graph.json","fetch_events":"https://pith.science/api/pith-number/2QER4INFRVNTCUQLSWE2Q4IM2H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2QER4INFRVNTCUQLSWE2Q4IM2H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2QER4INFRVNTCUQLSWE2Q4IM2H/action/storage_attestation","attest_author":"https://pith.science/pith/2QER4INFRVNTCUQLSWE2Q4IM2H/action/author_attestation","sign_citation":"https://pith.science/pith/2QER4INFRVNTCUQLSWE2Q4IM2H/action/citation_signature","submit_replication":"https://pith.science/pith/2QER4INFRVNTCUQLSWE2Q4IM2H/action/replication_record"}},"created_at":"2026-05-18T00:09:42.271264+00:00","updated_at":"2026-05-18T00:09:42.271264+00:00"}