{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XUSZYBCE5BQMTXZCXTVCWNIWBJ","short_pith_number":"pith:XUSZYBCE","schema_version":"1.0","canonical_sha256":"bd259c0444e860c9df22bcea2b35160a4141cd81c2dbae3f244213f8bea9dc4f","source":{"kind":"arxiv","id":"2506.14108","version":2},"attestation_state":"computed","paper":{"title":"$\\beta$-integrated local depth and corresponding partitioned local depth representation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexandre Leblanc, Paul D. McNicholas, Siyi Wang","submitted_at":"2025-06-17T01:59:41Z","abstract_excerpt":"A novel local depth definition, $\\beta$-integrated local depth ($\\beta$-ILD), is proposed as a generalization of the local depth introduced by Paindaveine and Van Bever \\cite{paindaveine2013depth}, designed to quantify the local centrality of data points. $\\beta$-ILD inherits desirable properties from global data depth and remains robust across varying locality levels. A partitioning approach for $\\beta$-ILD is introduced, leading to the construction of a matrix that quantifies the contribution of one point to another's local depth, providing a new interpretable measure of local centrality. Th"},"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":"2506.14108","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-17T01:59:41Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"ff2c73326ee871a35d548e3f41e52fcf92fc29b133d2b6b294f7d7ff0eff7b6e","abstract_canon_sha256":"66ea6ac1196acf012969f482ef639fb7abe0010961912f9fc981debac95776cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:25:12.893096Z","signature_b64":"U6joP0vYKf9E0RV7mM1vDMbZu+YzmSmOD7iil7Nhfz6eSoZZegIH1QspzZ6tOS2kGZBkg/UaWsywWg+3wTw9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd259c0444e860c9df22bcea2b35160a4141cd81c2dbae3f244213f8bea9dc4f","last_reissued_at":"2026-07-05T11:25:12.892573Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:25:12.892573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\beta$-integrated local depth and corresponding partitioned local depth representation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexandre Leblanc, Paul D. McNicholas, Siyi Wang","submitted_at":"2025-06-17T01:59:41Z","abstract_excerpt":"A novel local depth definition, $\\beta$-integrated local depth ($\\beta$-ILD), is proposed as a generalization of the local depth introduced by Paindaveine and Van Bever \\cite{paindaveine2013depth}, designed to quantify the local centrality of data points. $\\beta$-ILD inherits desirable properties from global data depth and remains robust across varying locality levels. A partitioning approach for $\\beta$-ILD is introduced, leading to the construction of a matrix that quantifies the contribution of one point to another's local depth, providing a new interpretable measure of local centrality. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.14108","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.14108/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.14108","created_at":"2026-07-05T11:25:12.892636+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.14108v2","created_at":"2026-07-05T11:25:12.892636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.14108","created_at":"2026-07-05T11:25:12.892636+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUSZYBCE5BQM","created_at":"2026-07-05T11:25:12.892636+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUSZYBCE5BQMTXZC","created_at":"2026-07-05T11:25:12.892636+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUSZYBCE","created_at":"2026-07-05T11:25:12.892636+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/XUSZYBCE5BQMTXZCXTVCWNIWBJ","json":"https://pith.science/pith/XUSZYBCE5BQMTXZCXTVCWNIWBJ.json","graph_json":"https://pith.science/api/pith-number/XUSZYBCE5BQMTXZCXTVCWNIWBJ/graph.json","events_json":"https://pith.science/api/pith-number/XUSZYBCE5BQMTXZCXTVCWNIWBJ/events.json","paper":"https://pith.science/paper/XUSZYBCE"},"agent_actions":{"view_html":"https://pith.science/pith/XUSZYBCE5BQMTXZCXTVCWNIWBJ","download_json":"https://pith.science/pith/XUSZYBCE5BQMTXZCXTVCWNIWBJ.json","view_paper":"https://pith.science/paper/XUSZYBCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.14108&json=true","fetch_graph":"https://pith.science/api/pith-number/XUSZYBCE5BQMTXZCXTVCWNIWBJ/graph.json","fetch_events":"https://pith.science/api/pith-number/XUSZYBCE5BQMTXZCXTVCWNIWBJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUSZYBCE5BQMTXZCXTVCWNIWBJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUSZYBCE5BQMTXZCXTVCWNIWBJ/action/storage_attestation","attest_author":"https://pith.science/pith/XUSZYBCE5BQMTXZCXTVCWNIWBJ/action/author_attestation","sign_citation":"https://pith.science/pith/XUSZYBCE5BQMTXZCXTVCWNIWBJ/action/citation_signature","submit_replication":"https://pith.science/pith/XUSZYBCE5BQMTXZCXTVCWNIWBJ/action/replication_record"}},"created_at":"2026-07-05T11:25:12.892636+00:00","updated_at":"2026-07-05T11:25:12.892636+00:00"}