{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:RR4CPJD72NNFJEJAAD3CBUU5DN","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":"056adab62adb8fa4fee42591815645fce7cfc261b77ba5944fe281819f9e8fee","cross_cats_sorted":["cs.CR","cs.LG","stat.ME","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-12-12T23:17:29Z","title_canon_sha256":"b9b2a9e741f21483f14c33f5caebe5277a863596ea4d7cba5d4ae97ec1a44452"},"schema_version":"1.0","source":{"id":"2312.07792","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.07792","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"2312.07792v3","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.07792","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"RR4CPJD72NNF","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"pith_short_16","alias_value":"RR4CPJD72NNFJEJA","created_at":"2026-07-05T08:47:09Z"},{"alias_kind":"pith_short_8","alias_value":"RR4CPJD7","created_at":"2026-07-05T08:47:09Z"}],"graph_snapshots":[{"event_id":"sha256:90d5025472dbe9828f45f9dda68114f78ab2cc7b9893d62072517d09c8fe48de","target":"graph","created_at":"2026-07-05T08:47:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2312.07792/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop $(\\epsilon,\\delta)$-differentially private projection-depth-based medians using the propose-test-release (PTR) and exponential mechanisms. Under general conditions on the input parameters and the population measure, (e.g. we do not assume any moment bounds), we quantify the probability the test in PTR fails, as well as the cost of privacy via finite sample deviation bounds. Next, we show that when some observations are contaminated, the private projection-depth-based median does not break down, provided its input location and scale estimators do not break down. We demonstrate our ma","authors_text":"Dylan Spicker, Kelly Ramsay","cross_cats":["cs.CR","cs.LG","stat.ME","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-12-12T23:17:29Z","title":"Differentially private projection-depth-based medians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.07792","kind":"arxiv","version":3},"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:a3fdfdc44093e0aeddaf1befa183d8957268c446fbaf5e2c8e6a61ab858de148","target":"record","created_at":"2026-07-05T08:47:09Z","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":"056adab62adb8fa4fee42591815645fce7cfc261b77ba5944fe281819f9e8fee","cross_cats_sorted":["cs.CR","cs.LG","stat.ME","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-12-12T23:17:29Z","title_canon_sha256":"b9b2a9e741f21483f14c33f5caebe5277a863596ea4d7cba5d4ae97ec1a44452"},"schema_version":"1.0","source":{"id":"2312.07792","kind":"arxiv","version":3}},"canonical_sha256":"8c7827a47fd35a54912000f620d29d1b581f89d97040d63afbd1a984b6c7ebf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c7827a47fd35a54912000f620d29d1b581f89d97040d63afbd1a984b6c7ebf7","first_computed_at":"2026-07-05T08:47:09.291268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:47:09.291268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I9lIoKXGxKKM0iimU1G8d98MHGYC0n0J3F2bCzGJ6BRPe8AGembOmdce5K0Cl42DZZbljssvlMX0lBTAI3wcBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:47:09.291815Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.07792","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3fdfdc44093e0aeddaf1befa183d8957268c446fbaf5e2c8e6a61ab858de148","sha256:90d5025472dbe9828f45f9dda68114f78ab2cc7b9893d62072517d09c8fe48de"],"state_sha256":"5e5269117e520f96d4bf54198f6576d87a25d807ee41a2c3cd30de38b447b468"}