{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:LAQ7WN7PNHK5JKDTIE6Y7452AZ","short_pith_number":"pith:LAQ7WN7P","schema_version":"1.0","canonical_sha256":"5821fb37ef69d5d4a873413d8ff3ba067e017b4163c6e29a7d66c7df8c0cb6eb","source":{"kind":"arxiv","id":"1407.2023","version":1},"attestation_state":"computed","paper":{"title":"BMO-type norms related to the perimeter of sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alessio Figalli, Haim Brezis, Jean Bourgain, Luigi Ambrosio","submitted_at":"2014-07-08T10:14:24Z","abstract_excerpt":"In this paper we consider an isotropic variant of the $BMO$-type norm recently introduced by Bourgain, Brezis and Mironescu. We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions."},"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":"1407.2023","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-08T10:14:24Z","cross_cats_sorted":[],"title_canon_sha256":"02b57adb089a9f36f9778c4296c8cfcf3d1ec74c13c34389e12fb7f2b690ba8b","abstract_canon_sha256":"05d052d00faac2de1db6091a7560986144c52c8ac10fcfbba0022bc59ecb00eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:08.639347Z","signature_b64":"zAtp4ZfEUcZ6ez0R2heGDTCWapu6mNKT4JBvXh4JymYD0FWffL4kYPRh0fWAFXn01Nu6ZF4DXsKXvgH6NpAaBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5821fb37ef69d5d4a873413d8ff3ba067e017b4163c6e29a7d66c7df8c0cb6eb","last_reissued_at":"2026-05-18T02:48:08.638681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:08.638681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"BMO-type norms related to the perimeter of sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alessio Figalli, Haim Brezis, Jean Bourgain, Luigi Ambrosio","submitted_at":"2014-07-08T10:14:24Z","abstract_excerpt":"In this paper we consider an isotropic variant of the $BMO$-type norm recently introduced by Bourgain, Brezis and Mironescu. We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2023","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":"1407.2023","created_at":"2026-05-18T02:48:08.638779+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.2023v1","created_at":"2026-05-18T02:48:08.638779+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2023","created_at":"2026-05-18T02:48:08.638779+00:00"},{"alias_kind":"pith_short_12","alias_value":"LAQ7WN7PNHK5","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"LAQ7WN7PNHK5JKDT","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"LAQ7WN7P","created_at":"2026-05-18T12:28:35.611951+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/LAQ7WN7PNHK5JKDTIE6Y7452AZ","json":"https://pith.science/pith/LAQ7WN7PNHK5JKDTIE6Y7452AZ.json","graph_json":"https://pith.science/api/pith-number/LAQ7WN7PNHK5JKDTIE6Y7452AZ/graph.json","events_json":"https://pith.science/api/pith-number/LAQ7WN7PNHK5JKDTIE6Y7452AZ/events.json","paper":"https://pith.science/paper/LAQ7WN7P"},"agent_actions":{"view_html":"https://pith.science/pith/LAQ7WN7PNHK5JKDTIE6Y7452AZ","download_json":"https://pith.science/pith/LAQ7WN7PNHK5JKDTIE6Y7452AZ.json","view_paper":"https://pith.science/paper/LAQ7WN7P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.2023&json=true","fetch_graph":"https://pith.science/api/pith-number/LAQ7WN7PNHK5JKDTIE6Y7452AZ/graph.json","fetch_events":"https://pith.science/api/pith-number/LAQ7WN7PNHK5JKDTIE6Y7452AZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LAQ7WN7PNHK5JKDTIE6Y7452AZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LAQ7WN7PNHK5JKDTIE6Y7452AZ/action/storage_attestation","attest_author":"https://pith.science/pith/LAQ7WN7PNHK5JKDTIE6Y7452AZ/action/author_attestation","sign_citation":"https://pith.science/pith/LAQ7WN7PNHK5JKDTIE6Y7452AZ/action/citation_signature","submit_replication":"https://pith.science/pith/LAQ7WN7PNHK5JKDTIE6Y7452AZ/action/replication_record"}},"created_at":"2026-05-18T02:48:08.638779+00:00","updated_at":"2026-05-18T02:48:08.638779+00:00"}