{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:57XRZN2HTPN56HA7DGE234PPRC","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":"467f7429d76c619381a24f1b078da2aedf4eb80f567fac4f22fe4341e5f46505","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-11-21T15:12:23Z","title_canon_sha256":"c1fdca7317d0b05b9c813ffd0a9ac3d7f60f44c17ad7922c652b06e16f459cb2"},"schema_version":"1.0","source":{"id":"2411.14203","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14203","created_at":"2026-07-05T09:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14203v1","created_at":"2026-07-05T09:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14203","created_at":"2026-07-05T09:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"57XRZN2HTPN5","created_at":"2026-07-05T09:38:43Z"},{"alias_kind":"pith_short_16","alias_value":"57XRZN2HTPN56HA7","created_at":"2026-07-05T09:38:43Z"},{"alias_kind":"pith_short_8","alias_value":"57XRZN2H","created_at":"2026-07-05T09:38:43Z"}],"graph_snapshots":[{"event_id":"sha256:6e9a9ae15eec985a2aafac71630788121164e34d3455670cd5121897cea5a944","target":"graph","created_at":"2026-07-05T09:38:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.14203/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study piecewise quasiconformal covering maps of the unit circle. We provide sufficient conditions so that a conjugacy between two such dynamical systems has a quasiconformal or David extension to the unit disk. Our main result generalizes the main result of arXiv:2010.11256, which deals with piecewise analytic maps. As applications, we provide a classification of piecewise quasiconformal maps of the circle up to quasisymmetric conjugacy, we prove a general conformal mating theorem for Blaschke products, and we study the quasiconformal geometry of parabolic basins.","authors_text":"Dimitrios Ntalampekos, Yusheng Luo","cross_cats":["math.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-11-21T15:12:23Z","title":"Piecewise quasiconformal dynamical systems of the unit circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14203","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":"sha256:7cc45e5c353a3d72d65f36ee504df589976780c4802fc7e3ec3b9b56a879fad4","target":"record","created_at":"2026-07-05T09:38:43Z","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":"467f7429d76c619381a24f1b078da2aedf4eb80f567fac4f22fe4341e5f46505","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-11-21T15:12:23Z","title_canon_sha256":"c1fdca7317d0b05b9c813ffd0a9ac3d7f60f44c17ad7922c652b06e16f459cb2"},"schema_version":"1.0","source":{"id":"2411.14203","kind":"arxiv","version":1}},"canonical_sha256":"efef1cb7479bdbdf1c1f1989adf1ef888cee332f0b5141c861175062933f55cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efef1cb7479bdbdf1c1f1989adf1ef888cee332f0b5141c861175062933f55cb","first_computed_at":"2026-07-05T09:38:43.272834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:43.272834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tvl8qG1ZsH7CvzJrrX8/hAAMjR8hTQns0kNcaPS0IDbguhZSHGNNNOvTWwT0CuI4dtXz2o1f4jN0Knxi8oM9DA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:43.273346Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14203","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cc45e5c353a3d72d65f36ee504df589976780c4802fc7e3ec3b9b56a879fad4","sha256:6e9a9ae15eec985a2aafac71630788121164e34d3455670cd5121897cea5a944"],"state_sha256":"dcca1cc9e8db8890ee91eff85103929ca877a1582af1026093c32ba9703ca464"}