{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CW4RAIPPGCC5QBPRXDF2SOMTOL","short_pith_number":"pith:CW4RAIPP","schema_version":"1.0","canonical_sha256":"15b91021ef3085d805f1b8cba9399372edbab9b6375a77a4e0dc62bc188f60f1","source":{"kind":"arxiv","id":"1805.07373","version":1},"attestation_state":"computed","paper":{"title":"Approximate Data Depth Revisited","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"David Bremner, Rasoul Shahsavarifar","submitted_at":"2018-05-18T18:09:19Z","abstract_excerpt":"Halfspace depth and $\\beta$-skeleton depth are two types of depth functions in nonparametric data analysis. The halfspace depth of a query point $q\\in \\mathbb{R}^d$ with respect to $S\\subset\\mathbb{R}^d$ is the minimum portion of the elements of $S$ which are contained in a halfspace which passes through $q$. For $\\beta \\geq 1$, the $\\beta$-skeleton depth of $q$ with respect to $S$ is defined to be the total number of \\emph{$\\beta$-skeleton influence regions} that contain $q$, where each of these influence regions is the intersection of two hyperballs obtained from a pair of points in $S$. The"},"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":"1805.07373","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CG","submitted_at":"2018-05-18T18:09:19Z","cross_cats_sorted":[],"title_canon_sha256":"e5d379edecb19f58ddfe2d6f0ad8e2dfce4d3cd200d7b151f8261067e0b54689","abstract_canon_sha256":"0450594e5f6710d4b846efaf28540745b75342eabb06a7fc6ffff3196f75773e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:35.906550Z","signature_b64":"0f3eYccIiGLnBlJEBEzrNiFrSoSwypEzwiMKgaWOKuylxJGjUl+0YMlYPKa3r5AeqP4kWQbszA/TjwPoZW9/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15b91021ef3085d805f1b8cba9399372edbab9b6375a77a4e0dc62bc188f60f1","last_reissued_at":"2026-05-18T00:15:35.905792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:35.905792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximate Data Depth Revisited","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"David Bremner, Rasoul Shahsavarifar","submitted_at":"2018-05-18T18:09:19Z","abstract_excerpt":"Halfspace depth and $\\beta$-skeleton depth are two types of depth functions in nonparametric data analysis. The halfspace depth of a query point $q\\in \\mathbb{R}^d$ with respect to $S\\subset\\mathbb{R}^d$ is the minimum portion of the elements of $S$ which are contained in a halfspace which passes through $q$. For $\\beta \\geq 1$, the $\\beta$-skeleton depth of $q$ with respect to $S$ is defined to be the total number of \\emph{$\\beta$-skeleton influence regions} that contain $q$, where each of these influence regions is the intersection of two hyperballs obtained from a pair of points in $S$. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07373","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":"1805.07373","created_at":"2026-05-18T00:15:35.905938+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.07373v1","created_at":"2026-05-18T00:15:35.905938+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07373","created_at":"2026-05-18T00:15:35.905938+00:00"},{"alias_kind":"pith_short_12","alias_value":"CW4RAIPPGCC5","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"CW4RAIPPGCC5QBPR","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"CW4RAIPP","created_at":"2026-05-18T12:32:19.392346+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/CW4RAIPPGCC5QBPRXDF2SOMTOL","json":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL.json","graph_json":"https://pith.science/api/pith-number/CW4RAIPPGCC5QBPRXDF2SOMTOL/graph.json","events_json":"https://pith.science/api/pith-number/CW4RAIPPGCC5QBPRXDF2SOMTOL/events.json","paper":"https://pith.science/paper/CW4RAIPP"},"agent_actions":{"view_html":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL","download_json":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL.json","view_paper":"https://pith.science/paper/CW4RAIPP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.07373&json=true","fetch_graph":"https://pith.science/api/pith-number/CW4RAIPPGCC5QBPRXDF2SOMTOL/graph.json","fetch_events":"https://pith.science/api/pith-number/CW4RAIPPGCC5QBPRXDF2SOMTOL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/action/storage_attestation","attest_author":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/action/author_attestation","sign_citation":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/action/citation_signature","submit_replication":"https://pith.science/pith/CW4RAIPPGCC5QBPRXDF2SOMTOL/action/replication_record"}},"created_at":"2026-05-18T00:15:35.905938+00:00","updated_at":"2026-05-18T00:15:35.905938+00:00"}