{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2MEHTQ7XBY7I4EUL3L6JWNVOQ3","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":"364f351ed7953d905209bf36f4a58754fea11308c09217139918d4c1c8443e26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-18T05:12:06Z","title_canon_sha256":"31679631400f60df7c4ce50cb634730a7d379875934fd5c18d09af98103b743c"},"schema_version":"1.0","source":{"id":"1901.07398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07398","created_at":"2026-05-17T23:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07398v1","created_at":"2026-05-17T23:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07398","created_at":"2026-05-17T23:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"2MEHTQ7XBY7I","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2MEHTQ7XBY7I4EUL","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2MEHTQ7X","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:96f206fe2973e09d17fdb37a359eacdfd53a942afc70cb33fcec04caf8e12eef","target":"graph","created_at":"2026-05-17T23:55:47Z","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":"Let $X_1, \\ldots, X_n$ be independent non-negative random variables with cumulative distribution functions $F_1,F_2,\\ldots,F_n$, each satisfying certain (rather mild) conditions. We show that the median of $k$-th smallest order statistic of the vector $(X_1, \\ldots, X_n)$ is equivalent to the quantile of order $(k-1/2)/n$ with respect to the averaged distribution $F=\\frac{1}{n}\\sum_{i=1}^n F_i$.","authors_text":"Alexander E. Litvak, Konstantin Tikhomirov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-18T05:12:06Z","title":"Estimates for order statistics in terms of quantiles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07398","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:d3298c2de6ccc7ce75a908ec86641ecbb39a453e3c5da4b90a8509d28da953b3","target":"record","created_at":"2026-05-17T23:55:47Z","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":"364f351ed7953d905209bf36f4a58754fea11308c09217139918d4c1c8443e26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-01-18T05:12:06Z","title_canon_sha256":"31679631400f60df7c4ce50cb634730a7d379875934fd5c18d09af98103b743c"},"schema_version":"1.0","source":{"id":"1901.07398","kind":"arxiv","version":1}},"canonical_sha256":"d30879c3f70e3e8e128bdafc9b36ae86d07d425b25495f2a0a9d114649acea03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d30879c3f70e3e8e128bdafc9b36ae86d07d425b25495f2a0a9d114649acea03","first_computed_at":"2026-05-17T23:55:47.071713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:47.071713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tP0XEWxccPc0ZyvXrjDYmGms5ciElbPagZowWfhkSuZXqEO+g9q8a4BDBuMJQtdUhAsjfDHWR7UU1YXtG7nTCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:47.072294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3298c2de6ccc7ce75a908ec86641ecbb39a453e3c5da4b90a8509d28da953b3","sha256:96f206fe2973e09d17fdb37a359eacdfd53a942afc70cb33fcec04caf8e12eef"],"state_sha256":"07c257135d3b42aeccca19cc39a3cc5162228c04f578219a2255e6e5f755d393"}