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Portfolio selection.Journal of Finance,7, 77–91","work_id":"ab414fe1-7a73-48ec-b79f-97925fd3df74","year":1952}],"snapshot_sha256":"36907e226df78e77aa11a12802ac095d65ec00fff50c9f9f9ea00fe5da22dcc3"},"source":{"id":"2605.18370","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T23:58:16.710598Z","id":"406f7cd5-63e6-4231-8117-1d6bae4f230a","model_set":{"reader":"grok-4.3"},"one_line_summary":"Introduces Q-Q orthogonality to decompose the difference between empirical and population quantiles into direction-induced population movement, fixed-direction empirical fluctuation, and Bahadur remainder.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The error in a sample quantile for an estimated heavy-tailed projection decomposes into a direction-induced population shift, a fixed-direction empirical fluctuation, and a Bahadur remainder.","strongest_claim":"The difference between the empirical quantile computed using the estimated projection direction and the population quantile at the reference direction can be decomposed as hat q_alpha(hat w) - q_alpha(w_0) = D1 + D2 + D3, where D1 measures population quantile movement from perturbing the projection direction, D2 measures empirical quantile fluctuation with direction held fixed, and D3 is the Bahadur-type remainder.","weakest_assumption":"That the Q-Q orthogonality formulation cleanly separates projection-direction effects from quantile-threshold effects without requiring the global uniform-convergence condition that empirical-process theory normally imposes on local quantile-stability problems."}},"verdict_id":"406f7cd5-63e6-4231-8117-1d6bae4f230a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f1566eb650c41effced12eff3bb267554ab381ccf1f10e6eaaad742f3668d876","target":"record","created_at":"2026-05-20T00:05:57Z","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":"3c522fbc23153872bba7f9ebc02bea3504fac73ffbedd7f7209b0e0e14aac0bb","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-18T13:19:29Z","title_canon_sha256":"8a9618dd30e7441bac6d2b1693c4af7be94ea7fee742e8d63ec418dc812ed5da"},"schema_version":"1.0","source":{"id":"2605.18370","kind":"arxiv","version":1}},"canonical_sha256":"10fb9ce608c6437481295df044c44504a48a19f3066473888cc08ee583f2c7e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10fb9ce608c6437481295df044c44504a48a19f3066473888cc08ee583f2c7e1","first_computed_at":"2026-05-20T00:05:57.651996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:57.651996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gq8Gwyf3adC4bJQzFydCwvxowU90ItmQVnbyLW3+CuuzAvr+OcGG/kRij1A8W4Nq2SL8GEi5Zm+6UUonMuB8BA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:57.652719Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.18370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1566eb650c41effced12eff3bb267554ab381ccf1f10e6eaaad742f3668d876","sha256:f2f355e2aea1d0dac669afb8abfaa242495f994dde481b9437f3869e765e0aeb"],"state_sha256":"af205c0505f2a5d2e0bcf0119af3927dd7fa6e9f588686d0d3c9aa6b53fd2414"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ZRvfh/Xgo+sUibuVlH0Ybxi8kiLMjpVU/dqaCjuoptlohI7AvuYRInEV90bLlpjphwusTxNIwA2jNxl4uQhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:13:48.032384Z","bundle_sha256":"c3b49b020ca73ca474eeb9153718a6acd666ca010a7e335e1e3ae27ee7faedf1"}}