{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:N6VG43QTFVC4G7MRFWEVP5BRRE","short_pith_number":"pith:N6VG43QT","schema_version":"1.0","canonical_sha256":"6faa6e6e132d45c37d912d8957f4318901df38ee4024d6067c1a92fed1869505","source":{"kind":"arxiv","id":"1508.06241","version":1},"attestation_state":"computed","paper":{"title":"Fractional Perimeter and Nonlocal Minimal Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lombardini","submitted_at":"2015-08-25T18:26:05Z","abstract_excerpt":"This Master's thesis presents a study of the basic properties of the s-fractional perimeter and of the regularity theory of the corresponding s-minimal sets. In particular, we give full detailed proofs for all the Theorems contained in the article \"Nonlocal Minimal Surfaces\" by Caffarelli, Roquejoffre and Savin, where these s-minimal sets were introduced and studied for the first time."},"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":"1508.06241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T18:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"f4ed1203391c9ef55f7bec478868f9d617f84965ae5acc6cfd0391721d031ec1","abstract_canon_sha256":"0d961f57328b53fc4c1454a41a45f37a8cf803888eb854d353cc1f0d4b4e1a13"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:46.347693Z","signature_b64":"csR1DM9vervxj1Q4TX6bg5LbDHv3iNW3MhDhybehvyI+vFqgGwfCYeaFygNlLsKqZVDLmBxyuZs84GxqfItUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6faa6e6e132d45c37d912d8957f4318901df38ee4024d6067c1a92fed1869505","last_reissued_at":"2026-05-18T01:34:46.347178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:46.347178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional Perimeter and Nonlocal Minimal Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lombardini","submitted_at":"2015-08-25T18:26:05Z","abstract_excerpt":"This Master's thesis presents a study of the basic properties of the s-fractional perimeter and of the regularity theory of the corresponding s-minimal sets. In particular, we give full detailed proofs for all the Theorems contained in the article \"Nonlocal Minimal Surfaces\" by Caffarelli, Roquejoffre and Savin, where these s-minimal sets were introduced and studied for the first time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06241","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":"1508.06241","created_at":"2026-05-18T01:34:46.347254+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.06241v1","created_at":"2026-05-18T01:34:46.347254+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06241","created_at":"2026-05-18T01:34:46.347254+00:00"},{"alias_kind":"pith_short_12","alias_value":"N6VG43QTFVC4","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"N6VG43QTFVC4G7MR","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"N6VG43QT","created_at":"2026-05-18T12:29:32.376354+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/N6VG43QTFVC4G7MRFWEVP5BRRE","json":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE.json","graph_json":"https://pith.science/api/pith-number/N6VG43QTFVC4G7MRFWEVP5BRRE/graph.json","events_json":"https://pith.science/api/pith-number/N6VG43QTFVC4G7MRFWEVP5BRRE/events.json","paper":"https://pith.science/paper/N6VG43QT"},"agent_actions":{"view_html":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE","download_json":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE.json","view_paper":"https://pith.science/paper/N6VG43QT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.06241&json=true","fetch_graph":"https://pith.science/api/pith-number/N6VG43QTFVC4G7MRFWEVP5BRRE/graph.json","fetch_events":"https://pith.science/api/pith-number/N6VG43QTFVC4G7MRFWEVP5BRRE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/action/storage_attestation","attest_author":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/action/author_attestation","sign_citation":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/action/citation_signature","submit_replication":"https://pith.science/pith/N6VG43QTFVC4G7MRFWEVP5BRRE/action/replication_record"}},"created_at":"2026-05-18T01:34:46.347254+00:00","updated_at":"2026-05-18T01:34:46.347254+00:00"}