{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:F6RO6A4QTHIFDDDVB75BLFPU7G","short_pith_number":"pith:F6RO6A4Q","schema_version":"1.0","canonical_sha256":"2fa2ef039099d0518c750ffa1595f4f9a3ba4179f8e73f488da7f07e9a92d410","source":{"kind":"arxiv","id":"1506.04281","version":5},"attestation_state":"computed","paper":{"title":"Graph properties for nonlocal minimal surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Ovidiu Savin, Serena Dipierro","submitted_at":"2015-06-13T15:52:25Z","abstract_excerpt":"In this paper we show that a nonlocal minimal surface which is a graph outside a cylinder is in fact a graph in the whole of the space. As a consequence, in dimension~$3$, we show that the graph is smooth. The proofs rely on convolution techniques and appropriate integral estimates which show the pointwise validity of an Euler-Lagrange equation related to the nonlocal mean curvature."},"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":"1506.04281","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-13T15:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"052fc4b0b0a0fd580ce95901cfcad721f859803724e5184e3ab273a489d8a9ce","abstract_canon_sha256":"6b4a6d7cccddc9dd6780669fd6f4746c86017a8956499dddf383df8a38eb3d8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:32.663900Z","signature_b64":"5Qug0f4YU+mqfcxFsE5UP1YwMwXWdaIG5DD8KNZ0wGvQCWxN8kEMDJy0vEwXDvM+Dqw+NczzhYG1zdlSBx7DCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fa2ef039099d0518c750ffa1595f4f9a3ba4179f8e73f488da7f07e9a92d410","last_reissued_at":"2026-05-18T01:12:32.663386Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:32.663386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graph properties for nonlocal minimal surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Ovidiu Savin, Serena Dipierro","submitted_at":"2015-06-13T15:52:25Z","abstract_excerpt":"In this paper we show that a nonlocal minimal surface which is a graph outside a cylinder is in fact a graph in the whole of the space. As a consequence, in dimension~$3$, we show that the graph is smooth. The proofs rely on convolution techniques and appropriate integral estimates which show the pointwise validity of an Euler-Lagrange equation related to the nonlocal mean curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04281","kind":"arxiv","version":5},"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":"1506.04281","created_at":"2026-05-18T01:12:32.663469+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.04281v5","created_at":"2026-05-18T01:12:32.663469+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04281","created_at":"2026-05-18T01:12:32.663469+00:00"},{"alias_kind":"pith_short_12","alias_value":"F6RO6A4QTHIF","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"F6RO6A4QTHIFDDDV","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"F6RO6A4Q","created_at":"2026-05-18T12:29:19.899920+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/F6RO6A4QTHIFDDDVB75BLFPU7G","json":"https://pith.science/pith/F6RO6A4QTHIFDDDVB75BLFPU7G.json","graph_json":"https://pith.science/api/pith-number/F6RO6A4QTHIFDDDVB75BLFPU7G/graph.json","events_json":"https://pith.science/api/pith-number/F6RO6A4QTHIFDDDVB75BLFPU7G/events.json","paper":"https://pith.science/paper/F6RO6A4Q"},"agent_actions":{"view_html":"https://pith.science/pith/F6RO6A4QTHIFDDDVB75BLFPU7G","download_json":"https://pith.science/pith/F6RO6A4QTHIFDDDVB75BLFPU7G.json","view_paper":"https://pith.science/paper/F6RO6A4Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.04281&json=true","fetch_graph":"https://pith.science/api/pith-number/F6RO6A4QTHIFDDDVB75BLFPU7G/graph.json","fetch_events":"https://pith.science/api/pith-number/F6RO6A4QTHIFDDDVB75BLFPU7G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F6RO6A4QTHIFDDDVB75BLFPU7G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F6RO6A4QTHIFDDDVB75BLFPU7G/action/storage_attestation","attest_author":"https://pith.science/pith/F6RO6A4QTHIFDDDVB75BLFPU7G/action/author_attestation","sign_citation":"https://pith.science/pith/F6RO6A4QTHIFDDDVB75BLFPU7G/action/citation_signature","submit_replication":"https://pith.science/pith/F6RO6A4QTHIFDDDVB75BLFPU7G/action/replication_record"}},"created_at":"2026-05-18T01:12:32.663469+00:00","updated_at":"2026-05-18T01:12:32.663469+00:00"}