{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OIXQDCETAFJOPDP626U7YUQTBP","short_pith_number":"pith:OIXQDCET","schema_version":"1.0","canonical_sha256":"722f0188930152e78dfed7a9fc52130be4f51e1fbe81a1cff7906f1808980c57","source":{"kind":"arxiv","id":"1612.08295","version":2},"attestation_state":"computed","paper":{"title":"Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudia Bucur, Enrico Valdinoci, Luca Lombardini","submitted_at":"2016-12-25T20:50:27Z","abstract_excerpt":"In this paper, we consider the asymptotic behavior of the fractional mean curvature when $s\\to 0^+$. Moreover, we deal with the behavior of $s$-minimal surfaces when the fractional parameter $s\\in(0,1)$ is small, in a bounded and connected open set with $C^2$ boundary $\\Omega\\subset \\mathbb{R}^n$. We classify the behavior of $s$-minimal surfaces with respect to the fixed exterior data (i.e. the $s$-minimal set fixed outside of $\\Omega$). So, for $s$ small and depending on the data at infinity, the $s$-minimal set can be either empty in $\\Omega$, fill all $\\Omega$, or possibly develop a wildly "},"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":"1612.08295","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-25T20:50:27Z","cross_cats_sorted":[],"title_canon_sha256":"f51da910c0dca16e7b386fa336031fac50e9edd6966097c09d087be8d9bf11e0","abstract_canon_sha256":"4d49ea5a525f76a643992ac9267cdc0bcfe5a30324caa5600df368f253617b2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:32.697304Z","signature_b64":"WskfPiL8Ei1vTTjmKl6KqD/wM3f2zTbP2k+ZtRg/w4G/izmV+p0FJMJRH4DeJyetkRgXROGHEPGXLBBFfv3eCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"722f0188930152e78dfed7a9fc52130be4f51e1fbe81a1cff7906f1808980c57","last_reissued_at":"2026-05-18T00:03:32.696531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:32.696531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudia Bucur, Enrico Valdinoci, Luca Lombardini","submitted_at":"2016-12-25T20:50:27Z","abstract_excerpt":"In this paper, we consider the asymptotic behavior of the fractional mean curvature when $s\\to 0^+$. Moreover, we deal with the behavior of $s$-minimal surfaces when the fractional parameter $s\\in(0,1)$ is small, in a bounded and connected open set with $C^2$ boundary $\\Omega\\subset \\mathbb{R}^n$. We classify the behavior of $s$-minimal surfaces with respect to the fixed exterior data (i.e. the $s$-minimal set fixed outside of $\\Omega$). So, for $s$ small and depending on the data at infinity, the $s$-minimal set can be either empty in $\\Omega$, fill all $\\Omega$, or possibly develop a wildly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08295","kind":"arxiv","version":2},"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":"1612.08295","created_at":"2026-05-18T00:03:32.696634+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08295v2","created_at":"2026-05-18T00:03:32.696634+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08295","created_at":"2026-05-18T00:03:32.696634+00:00"},{"alias_kind":"pith_short_12","alias_value":"OIXQDCETAFJO","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OIXQDCETAFJOPDP6","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OIXQDCET","created_at":"2026-05-18T12:30:36.002864+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/OIXQDCETAFJOPDP626U7YUQTBP","json":"https://pith.science/pith/OIXQDCETAFJOPDP626U7YUQTBP.json","graph_json":"https://pith.science/api/pith-number/OIXQDCETAFJOPDP626U7YUQTBP/graph.json","events_json":"https://pith.science/api/pith-number/OIXQDCETAFJOPDP626U7YUQTBP/events.json","paper":"https://pith.science/paper/OIXQDCET"},"agent_actions":{"view_html":"https://pith.science/pith/OIXQDCETAFJOPDP626U7YUQTBP","download_json":"https://pith.science/pith/OIXQDCETAFJOPDP626U7YUQTBP.json","view_paper":"https://pith.science/paper/OIXQDCET","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08295&json=true","fetch_graph":"https://pith.science/api/pith-number/OIXQDCETAFJOPDP626U7YUQTBP/graph.json","fetch_events":"https://pith.science/api/pith-number/OIXQDCETAFJOPDP626U7YUQTBP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OIXQDCETAFJOPDP626U7YUQTBP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OIXQDCETAFJOPDP626U7YUQTBP/action/storage_attestation","attest_author":"https://pith.science/pith/OIXQDCETAFJOPDP626U7YUQTBP/action/author_attestation","sign_citation":"https://pith.science/pith/OIXQDCETAFJOPDP626U7YUQTBP/action/citation_signature","submit_replication":"https://pith.science/pith/OIXQDCETAFJOPDP626U7YUQTBP/action/replication_record"}},"created_at":"2026-05-18T00:03:32.696634+00:00","updated_at":"2026-05-18T00:03:32.696634+00:00"}