{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MZT5A6BRFHCQKTJ4ZZWUBGMRJ2","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":"8ebad033d17e7260d1429e85d62b409f6892a82c8e349386278fa7302ecaf7a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-23T17:46:23Z","title_canon_sha256":"e4b826f222d8907a69d76bceb5f20896144ba7abc83bc8b2611443ef7006cfa9"},"schema_version":"1.0","source":{"id":"1807.09159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09159","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09159v1","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09159","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"MZT5A6BRFHCQ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MZT5A6BRFHCQKTJ4","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MZT5A6BR","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:f0085e23ff9edc982a5cc1faac983d19530ae1e615c132d6d4173ea3dd383afa","target":"graph","created_at":"2026-05-17T23:50:59Z","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 study renormalizations of piecewise smooth homeomorphisms on the circle, by considering such maps as generalized interval exchange maps of genus one. Suppose that $Df$ is absolutely continuous on each interval of continuity and $D\\ln{Df}\\in \\mathbb{L}_{p}$ for some $p>1$. We prove, that under certain combinatorial assumptions on $f_{1}$ and $f_{2}$, corresponding renormalizations approach to each other in $C^{1+L_{1}}$-norm.","authors_text":"Abdumajid Begmatov, Kleyber Cunha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-23T17:46:23Z","title":"On the convergence of renormalizations of piecewise smooth homeomorphisms on the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09159","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":"sha256:19e19430a30ef16bd429ddc047cb1b934f7a8602fb80cd507184d27c76a269a4","target":"record","created_at":"2026-05-17T23:50:59Z","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":"8ebad033d17e7260d1429e85d62b409f6892a82c8e349386278fa7302ecaf7a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-23T17:46:23Z","title_canon_sha256":"e4b826f222d8907a69d76bceb5f20896144ba7abc83bc8b2611443ef7006cfa9"},"schema_version":"1.0","source":{"id":"1807.09159","kind":"arxiv","version":1}},"canonical_sha256":"6667d0783129c5054d3cce6d4099914eaf910709e4825210b624f919c35e3e49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6667d0783129c5054d3cce6d4099914eaf910709e4825210b624f919c35e3e49","first_computed_at":"2026-05-17T23:50:59.550570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:59.550570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g1/Aif5CrzA76lmFAVtNOvNqtci3jB4mjlq0nq4mfqjNkO+bE8z5nSsXUufZHynGQWuHKA8MV01sJEtbNyvyAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:59.551150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19e19430a30ef16bd429ddc047cb1b934f7a8602fb80cd507184d27c76a269a4","sha256:f0085e23ff9edc982a5cc1faac983d19530ae1e615c132d6d4173ea3dd383afa"],"state_sha256":"7a38a3e076dc04680c2ad844dfa1713eefd20790ef862e86c61f75781fe0760a"}