{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:U54CXQJCMFGWNNY6QSCSFQBHOL","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":"aa32c4d8a59446abe1b36ac8819f8e378c515d9caa3420100a508fcbb3f9f3fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2010-10-02T07:05:05Z","title_canon_sha256":"8136366128c6fa0a135fd7e918c6858d64294872892a35381ff8dfc434807e2a"},"schema_version":"1.0","source":{"id":"1010.0297","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0297","created_at":"2026-05-18T04:39:50Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0297v2","created_at":"2026-05-18T04:39:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0297","created_at":"2026-05-18T04:39:50Z"},{"alias_kind":"pith_short_12","alias_value":"U54CXQJCMFGW","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"U54CXQJCMFGWNNY6","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"U54CXQJC","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:e5689bdbafc03bd9eea2084dd8b269b75d52f27832a1f4f4dad8adddab349d54","target":"graph","created_at":"2026-05-18T04:39:50Z","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":"Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero if and only if the random vectors are independent. The notion of covariance with respect to a stochastic process is introduced, and it is shown that population distance covariance coincides with the covar","authors_text":"G\\'abor J. Sz\\'ekely, Maria L. Rizzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2010-10-02T07:05:05Z","title":"Brownian distance covariance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0297","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":"sha256:7cba896f0cf9a978aaf9df5b7e4856690defd903a6d786f09a5bb8e3fbb78b71","target":"record","created_at":"2026-05-18T04:39:50Z","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":"aa32c4d8a59446abe1b36ac8819f8e378c515d9caa3420100a508fcbb3f9f3fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2010-10-02T07:05:05Z","title_canon_sha256":"8136366128c6fa0a135fd7e918c6858d64294872892a35381ff8dfc434807e2a"},"schema_version":"1.0","source":{"id":"1010.0297","kind":"arxiv","version":2}},"canonical_sha256":"a7782bc122614d66b71e848522c02772eac8b49c2aabfbb191e1bff19a911730","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7782bc122614d66b71e848522c02772eac8b49c2aabfbb191e1bff19a911730","first_computed_at":"2026-05-18T04:39:50.026379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:50.026379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JzxlMG9VN4JvNwR++YJfTCjjSw4qfm6EuuCI69XcXkQkIVnX9NjI4vjNkft71Eh7hXBcvsQ088QGj/p8xROxCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:50.026870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0297","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cba896f0cf9a978aaf9df5b7e4856690defd903a6d786f09a5bb8e3fbb78b71","sha256:e5689bdbafc03bd9eea2084dd8b269b75d52f27832a1f4f4dad8adddab349d54"],"state_sha256":"d1cdf453aae36b45b2364d4b71700a44f18baec2f314994b5f41ee478427f371"}