{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KERVCZQFYFEMJFJG63764RL7JB","short_pith_number":"pith:KERVCZQF","canonical_record":{"source":{"id":"1410.1503","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2014-10-06T19:40:44Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"0025f54f5f401d32e9cfc3d7915039b1b6a3dd8e1f52a7d69fba147200336748","abstract_canon_sha256":"5be285bb3ffb5f372a60bd30043a54b3171fd5c38061f6aa9be778af6e5ae311"},"schema_version":"1.0"},"canonical_sha256":"5123516605c148c49526f6ffee457f4876285c477027de65d8285c22190ff5a7","source":{"kind":"arxiv","id":"1410.1503","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1503","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1503v1","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1503","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"KERVCZQFYFEM","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KERVCZQFYFEMJFJG","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KERVCZQF","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KERVCZQFYFEMJFJG63764RL7JB","target":"record","payload":{"canonical_record":{"source":{"id":"1410.1503","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2014-10-06T19:40:44Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"0025f54f5f401d32e9cfc3d7915039b1b6a3dd8e1f52a7d69fba147200336748","abstract_canon_sha256":"5be285bb3ffb5f372a60bd30043a54b3171fd5c38061f6aa9be778af6e5ae311"},"schema_version":"1.0"},"canonical_sha256":"5123516605c148c49526f6ffee457f4876285c477027de65d8285c22190ff5a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:02.007230Z","signature_b64":"bZTYZJKhJOGtO0GCy3Luqw1k2uyu4byyi4yoh6Wa3Hr6TNCDNQ4y5qRI6kfZFR0nWAAhEC+iIOVWwkN1ML7FDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5123516605c148c49526f6ffee457f4876285c477027de65d8285c22190ff5a7","last_reissued_at":"2026-05-18T02:41:02.006778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:02.006778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.1503","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gBvi4/1liUJ5wZ3AGagXFNcUEEP6P8BJ5HvQ3d27MurEjkV7pNw5lRBHhK9GfsfGbzWiXrlfn1lrCsPqAD2PAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:34:13.381463Z"},"content_sha256":"e9d62c523d8818605f5b01097109f83b65d519719ec18cf1e61e7f38ce3abae2","schema_version":"1.0","event_id":"sha256:e9d62c523d8818605f5b01097109f83b65d519719ec18cf1e61e7f38ce3abae2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KERVCZQFYFEMJFJG63764RL7JB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Computing for Distance Covariance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"stat.CO","authors_text":"Gabor J. Szekely, Xiaoming Huo","submitted_at":"2014-10-06T19:40:44Z","abstract_excerpt":"Distance covariance and distance correlation have been widely adopted in measuring dependence of a pair of random variables or random vectors. If the computation of distance covariance and distance correlation is implemented directly accordingly to its definition then its computational complexity is O($n^2$) which is a disadvantage compared to other faster methods. In this paper we show that the computation of distance covariance and distance correlation of real valued random variables can be implemented by an O(n log n) algorithm and this is comparable to other computationally efficient algor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1503","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zVkopf7xwiE7ISTCEf9fP7evylBB7zuXHI07N+CRfl3lX5wYLfBfiOQ5OEM8J0v/W50pz1IK19DvxnRbhbxcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:34:13.382078Z"},"content_sha256":"18ca457be858757c3fdea4663de23e45afabf40486c5bae9062a3c5e12d13fef","schema_version":"1.0","event_id":"sha256:18ca457be858757c3fdea4663de23e45afabf40486c5bae9062a3c5e12d13fef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KERVCZQFYFEMJFJG63764RL7JB/bundle.json","state_url":"https://pith.science/pith/KERVCZQFYFEMJFJG63764RL7JB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KERVCZQFYFEMJFJG63764RL7JB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T18:34:13Z","links":{"resolver":"https://pith.science/pith/KERVCZQFYFEMJFJG63764RL7JB","bundle":"https://pith.science/pith/KERVCZQFYFEMJFJG63764RL7JB/bundle.json","state":"https://pith.science/pith/KERVCZQFYFEMJFJG63764RL7JB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KERVCZQFYFEMJFJG63764RL7JB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KERVCZQFYFEMJFJG63764RL7JB","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":"5be285bb3ffb5f372a60bd30043a54b3171fd5c38061f6aa9be778af6e5ae311","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2014-10-06T19:40:44Z","title_canon_sha256":"0025f54f5f401d32e9cfc3d7915039b1b6a3dd8e1f52a7d69fba147200336748"},"schema_version":"1.0","source":{"id":"1410.1503","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1503","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1503v1","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1503","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"KERVCZQFYFEM","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KERVCZQFYFEMJFJG","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KERVCZQF","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:18ca457be858757c3fdea4663de23e45afabf40486c5bae9062a3c5e12d13fef","target":"graph","created_at":"2026-05-18T02:41:02Z","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 covariance and distance correlation have been widely adopted in measuring dependence of a pair of random variables or random vectors. If the computation of distance covariance and distance correlation is implemented directly accordingly to its definition then its computational complexity is O($n^2$) which is a disadvantage compared to other faster methods. In this paper we show that the computation of distance covariance and distance correlation of real valued random variables can be implemented by an O(n log n) algorithm and this is comparable to other computationally efficient algor","authors_text":"Gabor J. Szekely, Xiaoming Huo","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2014-10-06T19:40:44Z","title":"Fast Computing for Distance Covariance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1503","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:e9d62c523d8818605f5b01097109f83b65d519719ec18cf1e61e7f38ce3abae2","target":"record","created_at":"2026-05-18T02:41:02Z","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":"5be285bb3ffb5f372a60bd30043a54b3171fd5c38061f6aa9be778af6e5ae311","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2014-10-06T19:40:44Z","title_canon_sha256":"0025f54f5f401d32e9cfc3d7915039b1b6a3dd8e1f52a7d69fba147200336748"},"schema_version":"1.0","source":{"id":"1410.1503","kind":"arxiv","version":1}},"canonical_sha256":"5123516605c148c49526f6ffee457f4876285c477027de65d8285c22190ff5a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5123516605c148c49526f6ffee457f4876285c477027de65d8285c22190ff5a7","first_computed_at":"2026-05-18T02:41:02.006778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:02.006778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bZTYZJKhJOGtO0GCy3Luqw1k2uyu4byyi4yoh6Wa3Hr6TNCDNQ4y5qRI6kfZFR0nWAAhEC+iIOVWwkN1ML7FDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:02.007230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1503","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9d62c523d8818605f5b01097109f83b65d519719ec18cf1e61e7f38ce3abae2","sha256:18ca457be858757c3fdea4663de23e45afabf40486c5bae9062a3c5e12d13fef"],"state_sha256":"31823bfc93add7347fa616e1a45a9feec9ea8810875ac0c02664ca12d799b37f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1XQwSK5jasGZDlfVNK8Q4rCbZ+dz7/ZAi7yzd2KCA/m8rE7w2xfy/FaPtsgPdYU/p9f9j6YMfwotY7XSzvL7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:34:13.385284Z","bundle_sha256":"f9ca80c6e0e8b9b8c1a4f8d48576a168e5889470145e02ebf8d66a648fcf6979"}}