{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YOZT6NLF4YCZOH7LGKEW3I3YLO","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":"b52608d168951676845bd87a3cc0c0d8a54b38a659ad58f437006a63751d59e9","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-22T11:24:59Z","title_canon_sha256":"9ca40e7e7572f4c78c743cc2f42c2af5a309d15e8e0bccba5c1434d411ea472c"},"schema_version":"1.0","source":{"id":"1711.08232","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.08232","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1711.08232v4","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08232","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"YOZT6NLF4YCZ","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YOZT6NLF4YCZOH7L","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YOZT6NLF","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:e1e90cfc63147d9f134c70fc4f70d6a42a251f7cb37d622ac282ee6a886aa6d6","target":"graph","created_at":"2026-05-17T23:44:59Z","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 consider the class of measurable functions defined in all of $\\mathbb{R}^n$ that give rise to a nonlocal minimal graph over a ball of $\\mathbb{R}^n$. We establish that the gradient of any such function is bounded in the interior of the ball by a power of its oscillation. This estimate, together with previously known results, leads to the $C^\\infty$ regularity of the function in the ball. While the smoothness of nonlocal minimal graphs was known for $n = 1, 2$ (but without a quantitative bound), in higher dimensions only their continuity had been established.\n  To prove the gradient bound, w","authors_text":"Matteo Cozzi, Xavier Cabre","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-22T11:24:59Z","title":"A gradient estimate for nonlocal minimal graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08232","kind":"arxiv","version":4},"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:bf268511d28242163f2432af1810581a4a18469bef5064d62ff102903c6dd822","target":"record","created_at":"2026-05-17T23:44:59Z","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":"b52608d168951676845bd87a3cc0c0d8a54b38a659ad58f437006a63751d59e9","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-22T11:24:59Z","title_canon_sha256":"9ca40e7e7572f4c78c743cc2f42c2af5a309d15e8e0bccba5c1434d411ea472c"},"schema_version":"1.0","source":{"id":"1711.08232","kind":"arxiv","version":4}},"canonical_sha256":"c3b33f3565e605971feb32896da3785bbf8fb5eab6a9cb77f8b7ed632b099ed3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3b33f3565e605971feb32896da3785bbf8fb5eab6a9cb77f8b7ed632b099ed3","first_computed_at":"2026-05-17T23:44:59.970062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:59.970062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jD4ZBUB81DXLuhlkklhcqQisXCmm8n/Lr+Wy7uxZ4ctrPOLjC7aQkLR1G9iFm4ZCm9kow68N6WdPXi5ksxdRAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:59.970838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.08232","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf268511d28242163f2432af1810581a4a18469bef5064d62ff102903c6dd822","sha256:e1e90cfc63147d9f134c70fc4f70d6a42a251f7cb37d622ac282ee6a886aa6d6"],"state_sha256":"c3f094786eb0b96f8347a34acf530e3e95d4984147fe2508c882404e0def8cd4"}