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Here $\\epsilon>0$ depends explicitly on the ellipticity bounds of ${\\cal A}$. The condition ``is linear at $\\infty$'' is necessary - the result is false for the equation $f_\\zbar = k|f_z|$, for any $0<k<1$, ($k=0$ is Weyl's lemma).\n  We discuss the subsequent higher regularity imp"},"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":"1903.01008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-03T22:47:04Z","cross_cats_sorted":[],"title_canon_sha256":"3458afdf8b859601da57b1190a661916cf8a12f525455cc26cb754e408e99f9c","abstract_canon_sha256":"b6c68abf1a3a482f18d229fa005aa4519a7c817ad32087a74758d3ac9c2c4b0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:12.555211Z","signature_b64":"2UjGZI2C0b47BJQNQrS4nk8yaMbWJ8d4Ey0aqmD4W0002FkUtmilefO39MXDszhZGNav+0t6UHgQULI60PTWCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad2261a74d36053eeb6658b777b82c16b05f5570fd5ec42ba38729544ea4a997","last_reissued_at":"2026-05-17T23:52:12.554499Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:12.554499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Super regularity for Beltrami systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaven J. 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The condition ``is linear at $\\infty$'' is necessary - the result is false for the equation $f_\\zbar = k|f_z|$, for any $0<k<1$, ($k=0$ is Weyl's lemma).\n  We discuss the subsequent higher regularity imp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01008","kind":"arxiv","version":1},"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":"1903.01008","created_at":"2026-05-17T23:52:12.554591+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.01008v1","created_at":"2026-05-17T23:52:12.554591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01008","created_at":"2026-05-17T23:52:12.554591+00:00"},{"alias_kind":"pith_short_12","alias_value":"VURGDJ2NGYCT","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"VURGDJ2NGYCT523G","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"VURGDJ2N","created_at":"2026-05-18T12:33:30.264802+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/VURGDJ2NGYCT523GLC3XPOBMC2","json":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2.json","graph_json":"https://pith.science/api/pith-number/VURGDJ2NGYCT523GLC3XPOBMC2/graph.json","events_json":"https://pith.science/api/pith-number/VURGDJ2NGYCT523GLC3XPOBMC2/events.json","paper":"https://pith.science/paper/VURGDJ2N"},"agent_actions":{"view_html":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2","download_json":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2.json","view_paper":"https://pith.science/paper/VURGDJ2N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.01008&json=true","fetch_graph":"https://pith.science/api/pith-number/VURGDJ2NGYCT523GLC3XPOBMC2/graph.json","fetch_events":"https://pith.science/api/pith-number/VURGDJ2NGYCT523GLC3XPOBMC2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2/action/storage_attestation","attest_author":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2/action/author_attestation","sign_citation":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2/action/citation_signature","submit_replication":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2/action/replication_record"}},"created_at":"2026-05-17T23:52:12.554591+00:00","updated_at":"2026-05-17T23:52:12.554591+00:00"}