{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LL6ARLWLSOWCXJM4YSMSE6EAR2","short_pith_number":"pith:LL6ARLWL","canonical_record":{"source":{"id":"1604.07104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-25T01:49:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"d907fb364a71a40f07fdbd65b0fcc82c1092d76ad3c641d85223f6daffabdfcc","abstract_canon_sha256":"0a9b6a270f04189b3127fc7ae87ca83f23f02c8659985e4d3243373e4379d942"},"schema_version":"1.0"},"canonical_sha256":"5afc08aecb93ac2ba59cc4992278808e8e0522a80fb5e5998535d7e67859d3bc","source":{"kind":"arxiv","id":"1604.07104","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07104","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07104v1","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07104","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"LL6ARLWLSOWC","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LL6ARLWLSOWCXJM4","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LL6ARLWL","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LL6ARLWLSOWCXJM4YSMSE6EAR2","target":"record","payload":{"canonical_record":{"source":{"id":"1604.07104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-25T01:49:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"d907fb364a71a40f07fdbd65b0fcc82c1092d76ad3c641d85223f6daffabdfcc","abstract_canon_sha256":"0a9b6a270f04189b3127fc7ae87ca83f23f02c8659985e4d3243373e4379d942"},"schema_version":"1.0"},"canonical_sha256":"5afc08aecb93ac2ba59cc4992278808e8e0522a80fb5e5998535d7e67859d3bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:23.039553Z","signature_b64":"58QEmN7RDW0FulJYB15T3fin0BF7AqFdnpNm+C2KxvZK409M7YEy+uM3W8UMZObblnq6ro9fTJoPOp1acX5wBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5afc08aecb93ac2ba59cc4992278808e8e0522a80fb5e5998535d7e67859d3bc","last_reissued_at":"2026-05-18T01:16:23.039049Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:23.039049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.07104","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l72zDg/pRjfbMOXsGlrAh2naW3xlQ7SA96Tbn3dvjr1uL8bTz3YFETRLvFRMc6qKnVgTX7NzD44p6vVIrBIoAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:37:44.584044Z"},"content_sha256":"9766b692f05978c085d981ce530c5367f0b3b9b88e8a5d9e7bda9dd2d4a2c0db","schema_version":"1.0","event_id":"sha256:9766b692f05978c085d981ce530c5367f0b3b9b88e8a5d9e7bda9dd2d4a2c0db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LL6ARLWLSOWCXJM4YSMSE6EAR2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The limit of finite sample breakdown point of Tukey's halfspace median for general data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Shihua Luo, Xiaohui Liu, Yijun Zuo","submitted_at":"2016-04-25T01:49:34Z","abstract_excerpt":"Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey's halfspace median ($\\frac{1} {3}$) has been obtained in literature. In this paper, we establish the result under \\emph{weaker assumption} imposed on underlying distribution (halfspace symmetry) and on data set (not necessary in general position). The representation of Tukey's sample depth regions for data set \\emph{not necessary in general position} is also obtained, as a by-product of our derivation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07104","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ccuN+eZO+wCTeV8GuxnsONL5zGzGn6YmFrJJKVyIEJ49x9yyiiuyJ5bSaB2dgK2K+llxfUUYmJ2zo3T4Mf35BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:37:44.584743Z"},"content_sha256":"e49d4f392460093c3411bd929657bb6c8a4188b20af3fbf4be9af8481163208d","schema_version":"1.0","event_id":"sha256:e49d4f392460093c3411bd929657bb6c8a4188b20af3fbf4be9af8481163208d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LL6ARLWLSOWCXJM4YSMSE6EAR2/bundle.json","state_url":"https://pith.science/pith/LL6ARLWLSOWCXJM4YSMSE6EAR2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LL6ARLWLSOWCXJM4YSMSE6EAR2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T21:37:44Z","links":{"resolver":"https://pith.science/pith/LL6ARLWLSOWCXJM4YSMSE6EAR2","bundle":"https://pith.science/pith/LL6ARLWLSOWCXJM4YSMSE6EAR2/bundle.json","state":"https://pith.science/pith/LL6ARLWLSOWCXJM4YSMSE6EAR2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LL6ARLWLSOWCXJM4YSMSE6EAR2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LL6ARLWLSOWCXJM4YSMSE6EAR2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0a9b6a270f04189b3127fc7ae87ca83f23f02c8659985e4d3243373e4379d942","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-25T01:49:34Z","title_canon_sha256":"d907fb364a71a40f07fdbd65b0fcc82c1092d76ad3c641d85223f6daffabdfcc"},"schema_version":"1.0","source":{"id":"1604.07104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07104","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07104v1","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07104","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"LL6ARLWLSOWC","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LL6ARLWLSOWCXJM4","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LL6ARLWL","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:e49d4f392460093c3411bd929657bb6c8a4188b20af3fbf4be9af8481163208d","target":"graph","created_at":"2026-05-18T01:16:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Under special conditions on data set and underlying distribution, the limit of finite sample breakdown point of Tukey's halfspace median ($\\frac{1} {3}$) has been obtained in literature. In this paper, we establish the result under \\emph{weaker assumption} imposed on underlying distribution (halfspace symmetry) and on data set (not necessary in general position). The representation of Tukey's sample depth regions for data set \\emph{not necessary in general position} is also obtained, as a by-product of our derivation.","authors_text":"Shihua Luo, Xiaohui Liu, Yijun Zuo","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-25T01:49:34Z","title":"The limit of finite sample breakdown point of Tukey's halfspace median for general data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07104","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9766b692f05978c085d981ce530c5367f0b3b9b88e8a5d9e7bda9dd2d4a2c0db","target":"record","created_at":"2026-05-18T01:16:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0a9b6a270f04189b3127fc7ae87ca83f23f02c8659985e4d3243373e4379d942","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-04-25T01:49:34Z","title_canon_sha256":"d907fb364a71a40f07fdbd65b0fcc82c1092d76ad3c641d85223f6daffabdfcc"},"schema_version":"1.0","source":{"id":"1604.07104","kind":"arxiv","version":1}},"canonical_sha256":"5afc08aecb93ac2ba59cc4992278808e8e0522a80fb5e5998535d7e67859d3bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5afc08aecb93ac2ba59cc4992278808e8e0522a80fb5e5998535d7e67859d3bc","first_computed_at":"2026-05-18T01:16:23.039049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:23.039049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"58QEmN7RDW0FulJYB15T3fin0BF7AqFdnpNm+C2KxvZK409M7YEy+uM3W8UMZObblnq6ro9fTJoPOp1acX5wBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:23.039553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.07104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9766b692f05978c085d981ce530c5367f0b3b9b88e8a5d9e7bda9dd2d4a2c0db","sha256:e49d4f392460093c3411bd929657bb6c8a4188b20af3fbf4be9af8481163208d"],"state_sha256":"bb37ec6813ffb956d957a8a46c40e680a59df542194a5773a893ccf50fb1357b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fMSGEloR0wLJzaaH8eV7iOLy0E+uB9acoDhO7mRgLRLnVMkIDwLWGNsAeJ/dmFJhsi0ZJJw9i4rkwsw7mIIoCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T21:37:44.589634Z","bundle_sha256":"d15f6781c78b5524fb29909eb151355fadc48cea27ce4f52ff880e748dc40dbb"}}