{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZZUIVCL4CESYYNDWXDNZO57SMU","short_pith_number":"pith:ZZUIVCL4","schema_version":"1.0","canonical_sha256":"ce688a897c11258c3476b8db9777f2652bd33bcc291e494d2b1178d535c5f703","source":{"kind":"arxiv","id":"1603.08460","version":3},"attestation_state":"computed","paper":{"title":"On boundary detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alejandro Cholaquidis, Catherine Aaron","submitted_at":"2016-03-28T17:48:10Z","abstract_excerpt":"Given a sample of a random variable supported by a smooth compact manifold $M\\subset \\mathbb{R}^d$, we propose a test to decide whether the boundary of $M$ is empty or not with no preliminary support estimation. The test statistic is based on the maximal distance between a sample point and the average of its $k_n$-nearest neighbors. We prove that the level of the test can be estimated, that, with probability one, its power is one for $n$ large enough, and that there exists a consistent decision rule. Heuristics for choosing a convenient value for the $k_n$ parameter and identifying observation"},"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":"1603.08460","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-28T17:48:10Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"afd7415a04711c707907a79b8a9a50759318c78bca4287f8d7cb368874aa7d8d","abstract_canon_sha256":"511a81eac8e2f2eda91baa3b2a4a5b0578e1ebe8f3e5d2568e10a2c375e9306a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:37.419285Z","signature_b64":"Sg2OmxC6FXbwqs+bsIbrchNbop3A06s0WFV901EW6dGQ/3LYUbdUfezt6OA9R8kumMlv7HULin7zlxvfUyZMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce688a897c11258c3476b8db9777f2652bd33bcc291e494d2b1178d535c5f703","last_reissued_at":"2026-05-17T23:39:37.418724Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:37.418724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On boundary detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alejandro Cholaquidis, Catherine Aaron","submitted_at":"2016-03-28T17:48:10Z","abstract_excerpt":"Given a sample of a random variable supported by a smooth compact manifold $M\\subset \\mathbb{R}^d$, we propose a test to decide whether the boundary of $M$ is empty or not with no preliminary support estimation. The test statistic is based on the maximal distance between a sample point and the average of its $k_n$-nearest neighbors. We prove that the level of the test can be estimated, that, with probability one, its power is one for $n$ large enough, and that there exists a consistent decision rule. Heuristics for choosing a convenient value for the $k_n$ parameter and identifying observation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08460","kind":"arxiv","version":3},"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":"1603.08460","created_at":"2026-05-17T23:39:37.418827+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.08460v3","created_at":"2026-05-17T23:39:37.418827+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08460","created_at":"2026-05-17T23:39:37.418827+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZZUIVCL4CESY","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZZUIVCL4CESYYNDW","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZZUIVCL4","created_at":"2026-05-18T12:30:55.937587+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/ZZUIVCL4CESYYNDWXDNZO57SMU","json":"https://pith.science/pith/ZZUIVCL4CESYYNDWXDNZO57SMU.json","graph_json":"https://pith.science/api/pith-number/ZZUIVCL4CESYYNDWXDNZO57SMU/graph.json","events_json":"https://pith.science/api/pith-number/ZZUIVCL4CESYYNDWXDNZO57SMU/events.json","paper":"https://pith.science/paper/ZZUIVCL4"},"agent_actions":{"view_html":"https://pith.science/pith/ZZUIVCL4CESYYNDWXDNZO57SMU","download_json":"https://pith.science/pith/ZZUIVCL4CESYYNDWXDNZO57SMU.json","view_paper":"https://pith.science/paper/ZZUIVCL4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.08460&json=true","fetch_graph":"https://pith.science/api/pith-number/ZZUIVCL4CESYYNDWXDNZO57SMU/graph.json","fetch_events":"https://pith.science/api/pith-number/ZZUIVCL4CESYYNDWXDNZO57SMU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZZUIVCL4CESYYNDWXDNZO57SMU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZZUIVCL4CESYYNDWXDNZO57SMU/action/storage_attestation","attest_author":"https://pith.science/pith/ZZUIVCL4CESYYNDWXDNZO57SMU/action/author_attestation","sign_citation":"https://pith.science/pith/ZZUIVCL4CESYYNDWXDNZO57SMU/action/citation_signature","submit_replication":"https://pith.science/pith/ZZUIVCL4CESYYNDWXDNZO57SMU/action/replication_record"}},"created_at":"2026-05-17T23:39:37.418827+00:00","updated_at":"2026-05-17T23:39:37.418827+00:00"}