{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UW6AZIPMR7CZWDVMW6TOBKAHJL","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":"e5614e0c3c11c678f083ec10cb1c15f2cc05492fdbce752c31f18b67d8d305a3","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-10-26T13:57:23Z","title_canon_sha256":"6cc19062bbb32478638a0847e72e2b9dd1f41e567016cbcdc3dfbac519359f3d"},"schema_version":"1.0","source":{"id":"1810.11332","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.11332","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1810.11332v2","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11332","created_at":"2026-05-17T23:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"UW6AZIPMR7CZ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UW6AZIPMR7CZWDVM","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UW6AZIPM","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:ed7ca60f5b517455cbb6eca5867879f4e471b3602ac32c2e2bf299a376621a68","target":"graph","created_at":"2026-05-17T23:54:39Z","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":"Classical dependence measures such as Pearson correlation, Spearman's $\\rho$, and Kendall's $\\tau$ can detect only monotonic or linear dependence. To overcome these limitations, Szekely et al.(2007) proposed distance covariance as a weighted $L_2$ distance between the joint characteristic function and the product of marginal distributions. The distance covariance is $0$ if and only if two random vectors ${X}$ and ${Y}$ are independent. This measure has the power to detect the presence of a dependence structure when the sample size is large enough. They further showed that the sample distance c","authors_text":"Arin Chaudhuri, Wenhao Hu","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-10-26T13:57:23Z","title":"A fast algorithm for computing distance correlation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11332","kind":"arxiv","version":2},"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":"sha256:428838dc66e82f553c7e3d80974212c2f1405d1b312c17e63ac63e0f674f6bac","target":"record","created_at":"2026-05-17T23:54:39Z","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":"e5614e0c3c11c678f083ec10cb1c15f2cc05492fdbce752c31f18b67d8d305a3","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2018-10-26T13:57:23Z","title_canon_sha256":"6cc19062bbb32478638a0847e72e2b9dd1f41e567016cbcdc3dfbac519359f3d"},"schema_version":"1.0","source":{"id":"1810.11332","kind":"arxiv","version":2}},"canonical_sha256":"a5bc0ca1ec8fc59b0eacb7a6e0a8074af965912e6f3afa05c978e6aac1602d8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5bc0ca1ec8fc59b0eacb7a6e0a8074af965912e6f3afa05c978e6aac1602d8d","first_computed_at":"2026-05-17T23:54:39.104120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:39.104120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FVJiIQEdTyhhhwd9Maxk3eJHS9VO1zKfyw02jZDvQF3To7P5b9MRqKA51sAkmnbFRSRqs29zntER8+JRTq3QBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:39.104752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.11332","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:428838dc66e82f553c7e3d80974212c2f1405d1b312c17e63ac63e0f674f6bac","sha256:ed7ca60f5b517455cbb6eca5867879f4e471b3602ac32c2e2bf299a376621a68"],"state_sha256":"ef7efecc5c1d614e44a9cf75e8c1e20c65e441d51f12539f9be57bc04a41ed0a"}