{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:EBV4ORISH7DVDJLWQYLGQV2IVV","short_pith_number":"pith:EBV4ORIS","schema_version":"1.0","canonical_sha256":"206bc745123fc751a5768616685748ad67a7f231e7c464f8cae206b454bea26f","source":{"kind":"arxiv","id":"1201.1171","version":1},"attestation_state":"computed","paper":{"title":"Some intriguing properties of Tukey's half-space depth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Anil K. Ghosh, Probal Chaudhuri, Subhajit Dutta","submitted_at":"2012-01-05T13:51:47Z","abstract_excerpt":"For multivariate data, Tukey's half-space depth is one of the most popular depth functions available in the literature. It is conceptually simple and satisfies several desirable properties of depth functions. The Tukey median, the multivariate median associated with the half-space depth, is also a well-known measure of center for multivariate data with several interesting properties. In this article, we derive and investigate some interesting properties of half-space depth and its associated multivariate median. These properties, some of which are counterintuitive, have important statistical c"},"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":"1201.1171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-05T13:51:47Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e247514f67a7b3ba087149cae3ccd3cecf76e46cc5cbeca26f3a06deeb21cd1d","abstract_canon_sha256":"70c4f8ad51c745d56cdb2f8bdacf3723281d2c373349b7d0ee614708e5f7a7cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:05.871543Z","signature_b64":"b/PJqATZbI4ZEubxcNSo1tgmkLCQ4YvPpvH3TH81MnWfQKDW25eng4VfnzT/aCsIaWKR+Es16Rp4owxqLoZAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"206bc745123fc751a5768616685748ad67a7f231e7c464f8cae206b454bea26f","last_reissued_at":"2026-05-18T04:05:05.870879Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:05.870879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some intriguing properties of Tukey's half-space depth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Anil K. Ghosh, Probal Chaudhuri, Subhajit Dutta","submitted_at":"2012-01-05T13:51:47Z","abstract_excerpt":"For multivariate data, Tukey's half-space depth is one of the most popular depth functions available in the literature. It is conceptually simple and satisfies several desirable properties of depth functions. The Tukey median, the multivariate median associated with the half-space depth, is also a well-known measure of center for multivariate data with several interesting properties. In this article, we derive and investigate some interesting properties of half-space depth and its associated multivariate median. These properties, some of which are counterintuitive, have important statistical c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1171","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":"1201.1171","created_at":"2026-05-18T04:05:05.870974+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.1171v1","created_at":"2026-05-18T04:05:05.870974+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1171","created_at":"2026-05-18T04:05:05.870974+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBV4ORISH7DV","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBV4ORISH7DVDJLW","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBV4ORIS","created_at":"2026-05-18T12:27:04.183437+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/EBV4ORISH7DVDJLWQYLGQV2IVV","json":"https://pith.science/pith/EBV4ORISH7DVDJLWQYLGQV2IVV.json","graph_json":"https://pith.science/api/pith-number/EBV4ORISH7DVDJLWQYLGQV2IVV/graph.json","events_json":"https://pith.science/api/pith-number/EBV4ORISH7DVDJLWQYLGQV2IVV/events.json","paper":"https://pith.science/paper/EBV4ORIS"},"agent_actions":{"view_html":"https://pith.science/pith/EBV4ORISH7DVDJLWQYLGQV2IVV","download_json":"https://pith.science/pith/EBV4ORISH7DVDJLWQYLGQV2IVV.json","view_paper":"https://pith.science/paper/EBV4ORIS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.1171&json=true","fetch_graph":"https://pith.science/api/pith-number/EBV4ORISH7DVDJLWQYLGQV2IVV/graph.json","fetch_events":"https://pith.science/api/pith-number/EBV4ORISH7DVDJLWQYLGQV2IVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBV4ORISH7DVDJLWQYLGQV2IVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBV4ORISH7DVDJLWQYLGQV2IVV/action/storage_attestation","attest_author":"https://pith.science/pith/EBV4ORISH7DVDJLWQYLGQV2IVV/action/author_attestation","sign_citation":"https://pith.science/pith/EBV4ORISH7DVDJLWQYLGQV2IVV/action/citation_signature","submit_replication":"https://pith.science/pith/EBV4ORISH7DVDJLWQYLGQV2IVV/action/replication_record"}},"created_at":"2026-05-18T04:05:05.870974+00:00","updated_at":"2026-05-18T04:05:05.870974+00:00"}