{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RL5YB6JLYCSABZBI3LAMVDEVZ2","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":"541acca7b087175d93d76516966f50e512d6afae2bfd3691306347076e137a43","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-12-23T12:32:47Z","title_canon_sha256":"4bf45f4cf9328e8d6334fed32785a32f7f2f56d0aac3483885e4cce426869def"},"schema_version":"1.0","source":{"id":"1112.5573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5573","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5573v1","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5573","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"RL5YB6JLYCSA","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RL5YB6JLYCSABZBI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RL5YB6JL","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:ceaee8d8a88aafd849a2729abebf3b273b281e54869342188178eb83ac25e493","target":"graph","created_at":"2026-05-18T04:05:46Z","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 obtain a priori estimates in $L^p(\\omega)$ for the generalized Beltrami equation, provided that the coefficients are compactly supported $VMO$ functions with the expected ellipticity condition, and the weight $\\omega$ lies in the Muckenhoupt class $A_p$. As an application, we obtain improved regularity for the jacobian of certain quasiconformal mappings.","authors_text":"Albert Clop, V\\'ictor Cruz","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-12-23T12:32:47Z","title":"Weighted estimates for Beltrami equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5573","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":"sha256:44f7c7fd518db9ca508d9f43f5f20765f6b6e9e28ee23ccbab92f10dfce2e02a","target":"record","created_at":"2026-05-18T04:05:46Z","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":"541acca7b087175d93d76516966f50e512d6afae2bfd3691306347076e137a43","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-12-23T12:32:47Z","title_canon_sha256":"4bf45f4cf9328e8d6334fed32785a32f7f2f56d0aac3483885e4cce426869def"},"schema_version":"1.0","source":{"id":"1112.5573","kind":"arxiv","version":1}},"canonical_sha256":"8afb80f92bc0a400e428dac0ca8c95ceb3f02894fd81f9e98e005e01727bea8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8afb80f92bc0a400e428dac0ca8c95ceb3f02894fd81f9e98e005e01727bea8c","first_computed_at":"2026-05-18T04:05:46.503986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:46.503986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cD+wE4d4tlONG/jC9ux6wO7AwJlJCT8R6CXoPjiWE3Ntg2BSYwPVuOpY1dAEhT2eBbDl3qNUOkuZX5D7b2YjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:46.504540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.5573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44f7c7fd518db9ca508d9f43f5f20765f6b6e9e28ee23ccbab92f10dfce2e02a","sha256:ceaee8d8a88aafd849a2729abebf3b273b281e54869342188178eb83ac25e493"],"state_sha256":"5aa4d5d17d3ae0686321e8bffdbe197b736b5e0c475bcc424a0ad533554dbc61"}