{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HIZBK4IRFPIKRWGX57DTFZ63BG","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":"183b1fab4acda861ae2aa7f903861ebc43ba9874e4e4b909825c2c95afe46d2f","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-07T20:16:25Z","title_canon_sha256":"19f0b7dd0ec4f54ab45eaf5f9021a87e878446f4a998651c5a9b491d88e802e8"},"schema_version":"1.0","source":{"id":"1502.02181","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02181","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02181v1","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02181","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"pith_short_12","alias_value":"HIZBK4IRFPIK","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HIZBK4IRFPIKRWGX","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HIZBK4IR","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:3ec459094ff238404b2ed2c74f658e498615f6f623e955e9fa6595a7e250743a","target":"graph","created_at":"2026-05-18T01:08:21Z","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 the relation between the geometric properties of a quasicircle~$\\Gamma$ and the complex dilatation~$\\mu$ of a quasiconformal mapping that maps the real line onto~$\\Gamma$. Denoting by~$S$ the Beurling transform, we characterize Bishop-Jones quasicircles in terms of the boundedness of the operator~$(I-\\mu S)$ on a particular weighted $L^2$~space, and chord-arc curves in terms of its invertibility. As an application we recover the~$L^2$ boundedness of the Cauchy integral on chord-arc curves.","authors_text":"K. Astala, M.J. Gonz\\'alez","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-07T20:16:25Z","title":"Chord-arc curves and the Beurling transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02181","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:fb12ee295a96f199c1187b5dd6f7a6ea9b6084d826e8d3026b6edcf656cb8a69","target":"record","created_at":"2026-05-18T01:08:21Z","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":"183b1fab4acda861ae2aa7f903861ebc43ba9874e4e4b909825c2c95afe46d2f","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-07T20:16:25Z","title_canon_sha256":"19f0b7dd0ec4f54ab45eaf5f9021a87e878446f4a998651c5a9b491d88e802e8"},"schema_version":"1.0","source":{"id":"1502.02181","kind":"arxiv","version":1}},"canonical_sha256":"3a321571112bd0a8d8d7efc732e7db0988dce949f38a21203a6c8389a3ec47a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a321571112bd0a8d8d7efc732e7db0988dce949f38a21203a6c8389a3ec47a5","first_computed_at":"2026-05-18T01:08:21.366926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:21.366926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RRZxCz05Tv2HOFv5f+rXxAu0a72BgtTA9m4+04epLsxleA0CDflXHPOEYiHDxTIE2gLIPaUIn1evQ+P8bil2Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:21.367429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02181","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb12ee295a96f199c1187b5dd6f7a6ea9b6084d826e8d3026b6edcf656cb8a69","sha256:3ec459094ff238404b2ed2c74f658e498615f6f623e955e9fa6595a7e250743a"],"state_sha256":"62ab4ca0ced3e06a6df0c050cad1bb0432c6af7964d99b5db22a79d9dc0862df"}