{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VTVU52UHFOWIAXVD6I5QUVSVDT","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":"f198e13d865d64d4759ae11add86a443cd263ceefae043db02990527587057ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-03T09:46:01Z","title_canon_sha256":"19bacbae1d93d392ebd25b67ffa623768920b32ff8c453061e48d545b0ee8700"},"schema_version":"1.0","source":{"id":"1806.00758","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00758","created_at":"2026-05-18T00:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00758v1","created_at":"2026-05-18T00:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00758","created_at":"2026-05-18T00:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"VTVU52UHFOWI","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VTVU52UHFOWIAXVD","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VTVU52UH","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:75f573be76730143cf2df0e069d9649170cff3bd6218836233c2089b6e4fa8e8","target":"graph","created_at":"2026-05-18T00:14:18Z","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 that a family of quasiregular mappings of a domain $\\Omega$ which are uniformly bounded in $L^p$ for some $p>0$ form a normal family. From this we show how an elliptic estimate on a functional differences implies all directional derivatives, and thus the complex gradient to be quasiregular. Consequently the function enjoys much higher regularity than apriori assumptions suggest.","authors_text":"Aimo Hinkkanen, Gaven Martin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-03T09:46:01Z","title":"Quasiregular families bounded in $L^p$ and elliptic estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00758","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":"sha256:08ddb5b625a01731ca7e0ff240ccc6838a2e2edb993986cc1461614f11dbc116","target":"record","created_at":"2026-05-18T00:14:18Z","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":"f198e13d865d64d4759ae11add86a443cd263ceefae043db02990527587057ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-03T09:46:01Z","title_canon_sha256":"19bacbae1d93d392ebd25b67ffa623768920b32ff8c453061e48d545b0ee8700"},"schema_version":"1.0","source":{"id":"1806.00758","kind":"arxiv","version":1}},"canonical_sha256":"aceb4eea872bac805ea3f23b0a56551cc6793fd19b96f654ca45279ef1c00686","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aceb4eea872bac805ea3f23b0a56551cc6793fd19b96f654ca45279ef1c00686","first_computed_at":"2026-05-18T00:14:18.539384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:18.539384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iePnRlzDt6kO622tB7ku7TpNZm0eVLpVAxm051u355iCo18VmvNOLinpVMNoC1SJEmz6m1yMD24ymj+e81bTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:18.539968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00758","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08ddb5b625a01731ca7e0ff240ccc6838a2e2edb993986cc1461614f11dbc116","sha256:75f573be76730143cf2df0e069d9649170cff3bd6218836233c2089b6e4fa8e8"],"state_sha256":"c62a43cfc3debc3198eb6ac78446b6f0644213eaab0efd37001cb289fd811f99"}