{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:U64BQ3LCT45CKAPMNESG4VW4V7","short_pith_number":"pith:U64BQ3LC","canonical_record":{"source":{"id":"2605.16219","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T17:30:42Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"755b550fefa83a3229943a55249775b536b79c942f70e32914de0eb1948e4f64","abstract_canon_sha256":"35b68a8ad7ab62f681937c8a53e9f7ea18864a8d32ef668ae49088e10d57a59c"},"schema_version":"1.0"},"canonical_sha256":"a7b8186d629f3a2501ec69246e56dcafd777affe517082ff6d6c0c3d8735f9f7","source":{"kind":"arxiv","id":"2605.16219","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16219","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16219v1","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16219","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_12","alias_value":"U64BQ3LCT45C","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_16","alias_value":"U64BQ3LCT45CKAPM","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_8","alias_value":"U64BQ3LC","created_at":"2026-05-20T00:01:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:U64BQ3LCT45CKAPMNESG4VW4V7","target":"record","payload":{"canonical_record":{"source":{"id":"2605.16219","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T17:30:42Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"755b550fefa83a3229943a55249775b536b79c942f70e32914de0eb1948e4f64","abstract_canon_sha256":"35b68a8ad7ab62f681937c8a53e9f7ea18864a8d32ef668ae49088e10d57a59c"},"schema_version":"1.0"},"canonical_sha256":"a7b8186d629f3a2501ec69246e56dcafd777affe517082ff6d6c0c3d8735f9f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:58.640728Z","signature_b64":"GN5lu2aMFdavYZGOQ4tNpl9neJDugTf9FKao17QgjDmAliiuZU98lKSKg39LND1wZFT1RjtJQRkoGtM7QEwLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7b8186d629f3a2501ec69246e56dcafd777affe517082ff6d6c0c3d8735f9f7","last_reissued_at":"2026-05-20T00:01:58.639880Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:58.639880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.16219","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":"2026-05-20T00:01:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o5cwph4+6HXzmzQL/51zU2vkpvYqqp3Xok0E+hMN/JSE19h+unzDCleRSqt3wSr3q1ntn/tkrbg0zNeGsNCYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:27:44.681398Z"},"content_sha256":"557bbce73176919684ddc84449fdf4e9d881d64d44feb9b74b5913ca5645c424","schema_version":"1.0","event_id":"sha256:557bbce73176919684ddc84449fdf4e9d881d64d44feb9b74b5913ca5645c424"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:U64BQ3LCT45CKAPMNESG4VW4V7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Privacy Price of Tail-Risk Learning: Effective Tail Sample Size in Differentially Private CVaR Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"El Mustapha Mansouri","submitted_at":"2026-05-15T17:30:42Z","abstract_excerpt":"Differential privacy changes the effective sample size governing CVaR learning. For tail mass $\\tau$, the privacy-relevant sample size is not $n$, but $n\\tau$; equivalently, the effective private tail sample size is $\\epsilon n\\tau$. Private CVaR excess risk decomposes into ordinary tail-risk statistical error and a privacy price. This decomposition is complete for scalar estimation and finite classes: scalar estimation has rate $\\Theta(B \\min\\{1,(n\\tau)^{-1/2}+(\\epsilon n\\tau)^{-1}\\})$, and finite classes of size $M$ have rate $\\Theta(B \\min\\{1,\\sqrt{\\log(2M)/(n\\tau)}+\\log(2M)/(\\epsilon n\\tau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.16219","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16219/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"shingle_duplication","ran_at":"2026-05-19T17:49:44.665869Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T17:49:44.154773Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:24.755655Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"external_links","ran_at":"2026-05-19T17:31:32.590878Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T17:22:05.919707Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.385490Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"062ca30d477c313755ca6a60a4ce3aa2515bfd0a17ce98e0dd9fff6e9d68a6ea"},"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":"2026-05-20T00:01:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8OzJFjTB+/b072SCPCrxjKpRaw1qYyXBJKo7HheppalU4aViOdqYDicKRB7tBOg3qb2N6d08BDr+/IbXza4EAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:27:44.682361Z"},"content_sha256":"889b9d6f962ab9911f01affd7623110ffd572f1d8490e46b785472535e7d7d45","schema_version":"1.0","event_id":"sha256:889b9d6f962ab9911f01affd7623110ffd572f1d8490e46b785472535e7d7d45"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U64BQ3LCT45CKAPMNESG4VW4V7/bundle.json","state_url":"https://pith.science/pith/U64BQ3LCT45CKAPMNESG4VW4V7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U64BQ3LCT45CKAPMNESG4VW4V7/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":"2026-06-11T08:27:44Z","links":{"resolver":"https://pith.science/pith/U64BQ3LCT45CKAPMNESG4VW4V7","bundle":"https://pith.science/pith/U64BQ3LCT45CKAPMNESG4VW4V7/bundle.json","state":"https://pith.science/pith/U64BQ3LCT45CKAPMNESG4VW4V7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U64BQ3LCT45CKAPMNESG4VW4V7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:U64BQ3LCT45CKAPMNESG4VW4V7","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":"35b68a8ad7ab62f681937c8a53e9f7ea18864a8d32ef668ae49088e10d57a59c","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T17:30:42Z","title_canon_sha256":"755b550fefa83a3229943a55249775b536b79c942f70e32914de0eb1948e4f64"},"schema_version":"1.0","source":{"id":"2605.16219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16219","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16219v1","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16219","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_12","alias_value":"U64BQ3LCT45C","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_16","alias_value":"U64BQ3LCT45CKAPM","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_8","alias_value":"U64BQ3LC","created_at":"2026-05-20T00:01:58Z"}],"graph_snapshots":[{"event_id":"sha256:889b9d6f962ab9911f01affd7623110ffd572f1d8490e46b785472535e7d7d45","target":"graph","created_at":"2026-05-20T00:01:58Z","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":[{"findings_count":0,"name":"shingle_duplication","ran_at":"2026-05-19T17:49:44.665869Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"citation_quote_validity","ran_at":"2026-05-19T17:49:44.154773Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:24.755655Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"external_links","ran_at":"2026-05-19T17:31:32.590878Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"cited_work_retraction","ran_at":"2026-05-19T17:22:05.919707Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.385490Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.16219/integrity.json","findings":[],"snapshot_sha256":"062ca30d477c313755ca6a60a4ce3aa2515bfd0a17ce98e0dd9fff6e9d68a6ea","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Differential privacy changes the effective sample size governing CVaR learning. For tail mass $\\tau$, the privacy-relevant sample size is not $n$, but $n\\tau$; equivalently, the effective private tail sample size is $\\epsilon n\\tau$. Private CVaR excess risk decomposes into ordinary tail-risk statistical error and a privacy price. This decomposition is complete for scalar estimation and finite classes: scalar estimation has rate $\\Theta(B \\min\\{1,(n\\tau)^{-1/2}+(\\epsilon n\\tau)^{-1}\\})$, and finite classes of size $M$ have rate $\\Theta(B \\min\\{1,\\sqrt{\\log(2M)/(n\\tau)}+\\log(2M)/(\\epsilon n\\tau","authors_text":"El Mustapha Mansouri","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T17:30:42Z","title":"The Privacy Price of Tail-Risk Learning: Effective Tail Sample Size in Differentially Private CVaR Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.16219","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":"sha256:557bbce73176919684ddc84449fdf4e9d881d64d44feb9b74b5913ca5645c424","target":"record","created_at":"2026-05-20T00:01:58Z","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":"35b68a8ad7ab62f681937c8a53e9f7ea18864a8d32ef668ae49088e10d57a59c","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-15T17:30:42Z","title_canon_sha256":"755b550fefa83a3229943a55249775b536b79c942f70e32914de0eb1948e4f64"},"schema_version":"1.0","source":{"id":"2605.16219","kind":"arxiv","version":1}},"canonical_sha256":"a7b8186d629f3a2501ec69246e56dcafd777affe517082ff6d6c0c3d8735f9f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7b8186d629f3a2501ec69246e56dcafd777affe517082ff6d6c0c3d8735f9f7","first_computed_at":"2026-05-20T00:01:58.639880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:58.639880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GN5lu2aMFdavYZGOQ4tNpl9neJDugTf9FKao17QgjDmAliiuZU98lKSKg39LND1wZFT1RjtJQRkoGtM7QEwLBg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:58.640728Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:557bbce73176919684ddc84449fdf4e9d881d64d44feb9b74b5913ca5645c424","sha256:889b9d6f962ab9911f01affd7623110ffd572f1d8490e46b785472535e7d7d45"],"state_sha256":"0fc68f8732b3d1088853bf626a4f91f572b968526d0dde6c4a52018bcd6e7aaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAYxDfu9vg4HQUJA2QHZA4R+H9BKIarO8QNE1TBa8V7koDI+HeW8vrpEeCRGs2wgT6Z1c/KSiZhUUL6Yt8CQCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:27:44.686190Z","bundle_sha256":"d14f10685c5745e96da45c126cb10041b2fa75c74b572453646ee57f28ee3e53"}}