{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:K7W2UY5QNKY7J4DKLT27CNZQGD","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":"6e6870e6c2315b1eb1a40aabbe09147118ed28c7c91547c8a185acae0281bba5","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-12-27T02:27:12Z","title_canon_sha256":"1ffb867d8f1a008699b7888a2cd2ba758d03a1cf8efcb4f33afea8b8cc181ecf"},"schema_version":"1.0","source":{"id":"1812.10596","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10596","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10596v1","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10596","created_at":"2026-05-17T23:57:20Z"},{"alias_kind":"pith_short_12","alias_value":"K7W2UY5QNKY7","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K7W2UY5QNKY7J4DK","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K7W2UY5Q","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:8e158ad6459ea3d34206838579fd276638ba938f77bbad772e58529a315f764c","target":"graph","created_at":"2026-05-17T23:57:20Z","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":"Assume that $X$ and $Y$ are independent random variables, each having a Cauchy distribution with a known median. Taking a random independent sample of size $n$ of each $X$ and $Y$, one can then compute their centralized empirical correlation coefficient $r$. Analytically investigating the sampling distribution of this $r$ appears possible only in the large $n$ limit; this is what we have done in this article, deriving several new and interesting results.","authors_text":"Jan Vrbik, Veson Lee","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-12-27T02:27:12Z","title":"Asymptotic Distribution of Centralized $r$ When Sampling from Cauchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10596","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":"sha256:23698a58245fd0b8e31b96a32f5577fa609b6e5719377b0993ec2cb74b1d48a7","target":"record","created_at":"2026-05-17T23:57:20Z","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":"6e6870e6c2315b1eb1a40aabbe09147118ed28c7c91547c8a185acae0281bba5","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-12-27T02:27:12Z","title_canon_sha256":"1ffb867d8f1a008699b7888a2cd2ba758d03a1cf8efcb4f33afea8b8cc181ecf"},"schema_version":"1.0","source":{"id":"1812.10596","kind":"arxiv","version":1}},"canonical_sha256":"57edaa63b06ab1f4f06a5cf5f1373030c1c1e4b7502956d6865bcadd688ea463","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57edaa63b06ab1f4f06a5cf5f1373030c1c1e4b7502956d6865bcadd688ea463","first_computed_at":"2026-05-17T23:57:20.550365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:20.550365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LihAgtpH7YkoLo1bd6Dqn+Qi44KxlLk11kLkSC+H5RDOcT/L4acTwT8CTh6t4amVb2TUPJHiFgNaUziXiTABDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:20.550882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10596","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23698a58245fd0b8e31b96a32f5577fa609b6e5719377b0993ec2cb74b1d48a7","sha256:8e158ad6459ea3d34206838579fd276638ba938f77bbad772e58529a315f764c"],"state_sha256":"e0b1bd5ecbfe5a5fbf55ff1d289e4df7c36d97cf1edffb7b86ded059a01965ad"}