{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VURGDJ2NGYCT523GLC3XPOBMC2","short_pith_number":"pith:VURGDJ2N","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"},"canonical_sha256":"ad2261a74d36053eeb6658b777b82c16b05f5570fd5ec42ba38729544ea4a997","source":{"kind":"arxiv","id":"1903.01008","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01008","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01008v1","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01008","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"VURGDJ2NGYCT","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VURGDJ2NGYCT523G","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VURGDJ2N","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VURGDJ2NGYCT523GLC3XPOBMC2","target":"record","payload":{"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"},"canonical_sha256":"ad2261a74d36053eeb6658b777b82c16b05f5570fd5ec42ba38729544ea4a997","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"},"source_kind":"arxiv","source_id":"1903.01008","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"osNVJ1HIZ4JXsY2Zq673YvYRRySEO2hrOCXeT3kVHu24CEZ+8VV04KH2UgWCZz8bjv5fv1DwthDON517FlbHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:39:24.586766Z"},"content_sha256":"70aedf4fff1342f9e2c76f720e549bf2c74d3c53a6fc9fdc2d72d4b4144eacca","schema_version":"1.0","event_id":"sha256:70aedf4fff1342f9e2c76f720e549bf2c74d3c53a6fc9fdc2d72d4b4144eacca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VURGDJ2NGYCT523GLC3XPOBMC2","target":"graph","payload":{"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. Martin","submitted_at":"2019-03-03T22:47:04Z","abstract_excerpt":"We prove a surprising higher regularity for solutions to the nonlinear elliptic autonomous Beltrami equation in a planar domain $\\Omega$, \\[ f_\\zbar = {\\cal A}(f_z) \\hskip15pt a.e.\\;\\; z\\in \\Omega, \\] when ${\\cal A}$ is linear at $\\infty$. Namely $W^{1,1}_{loc}(\\Omega)$ solutions are $W^{2,2+\\epsilon}_{loc}(\\Omega)$. 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"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fo/fybPmtIVw0LrrXAw8aU/dCFl4IGdoGTGUyXEoRcI+d7fUqGR9USgTmTR49YUYD0Ax+s7tu7FE8qXql1yzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:39:24.587418Z"},"content_sha256":"9d41536daf8e8d2d78dd224368b2f16b42cb7d8003d340eb07bb2998a5fcf0c7","schema_version":"1.0","event_id":"sha256:9d41536daf8e8d2d78dd224368b2f16b42cb7d8003d340eb07bb2998a5fcf0c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2/bundle.json","state_url":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VURGDJ2NGYCT523GLC3XPOBMC2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T05:39:24Z","links":{"resolver":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2","bundle":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2/bundle.json","state":"https://pith.science/pith/VURGDJ2NGYCT523GLC3XPOBMC2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VURGDJ2NGYCT523GLC3XPOBMC2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VURGDJ2NGYCT523GLC3XPOBMC2","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":"b6c68abf1a3a482f18d229fa005aa4519a7c817ad32087a74758d3ac9c2c4b0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-03T22:47:04Z","title_canon_sha256":"3458afdf8b859601da57b1190a661916cf8a12f525455cc26cb754e408e99f9c"},"schema_version":"1.0","source":{"id":"1903.01008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01008","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01008v1","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01008","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"VURGDJ2NGYCT","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VURGDJ2NGYCT523G","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VURGDJ2N","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:9d41536daf8e8d2d78dd224368b2f16b42cb7d8003d340eb07bb2998a5fcf0c7","target":"graph","created_at":"2026-05-17T23:52:12Z","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 prove a surprising higher regularity for solutions to the nonlinear elliptic autonomous Beltrami equation in a planar domain $\\Omega$, \\[ f_\\zbar = {\\cal A}(f_z) \\hskip15pt a.e.\\;\\; z\\in \\Omega, \\] when ${\\cal A}$ is linear at $\\infty$. Namely $W^{1,1}_{loc}(\\Omega)$ solutions are $W^{2,2+\\epsilon}_{loc}(\\Omega)$. 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","authors_text":"Gaven J. Martin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-03T22:47:04Z","title":"Super regularity for Beltrami systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01008","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":"sha256:70aedf4fff1342f9e2c76f720e549bf2c74d3c53a6fc9fdc2d72d4b4144eacca","target":"record","created_at":"2026-05-17T23:52:12Z","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":"b6c68abf1a3a482f18d229fa005aa4519a7c817ad32087a74758d3ac9c2c4b0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-03T22:47:04Z","title_canon_sha256":"3458afdf8b859601da57b1190a661916cf8a12f525455cc26cb754e408e99f9c"},"schema_version":"1.0","source":{"id":"1903.01008","kind":"arxiv","version":1}},"canonical_sha256":"ad2261a74d36053eeb6658b777b82c16b05f5570fd5ec42ba38729544ea4a997","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad2261a74d36053eeb6658b777b82c16b05f5570fd5ec42ba38729544ea4a997","first_computed_at":"2026-05-17T23:52:12.554499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:12.554499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2UjGZI2C0b47BJQNQrS4nk8yaMbWJ8d4Ey0aqmD4W0002FkUtmilefO39MXDszhZGNav+0t6UHgQULI60PTWCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:12.555211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.01008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70aedf4fff1342f9e2c76f720e549bf2c74d3c53a6fc9fdc2d72d4b4144eacca","sha256:9d41536daf8e8d2d78dd224368b2f16b42cb7d8003d340eb07bb2998a5fcf0c7"],"state_sha256":"c5de2a928401df2538999be14e241b8317a501af98e4b431a7c8634882adecb8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9hRGDOyDJS1Qlx3TuOeecQ1Wt8ipu4Ewtjuj6eOtK8nMAC8tEpEcUbtVBXhOpW3darB5XyyG6Wl23qWpn/uRDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:39:24.590623Z","bundle_sha256":"de275305c12c84ed27500538e659fceee9df767b4a9d8d152a8baf4470a6500b"}}