{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:YSIX27XIWNNEYEWIYZ43KCYDCU","short_pith_number":"pith:YSIX27XI","canonical_record":{"source":{"id":"2111.15567","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-11-30T17:00:52Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5f680a1e0ed7d277879b4eaa227d52a12ca3ffa5e8f34fddcbc5a06a9f2bdc00","abstract_canon_sha256":"119ef40962fe34998faf130a3a0ef93ec39aedf5e29c82648c76fde66f008c7a"},"schema_version":"1.0"},"canonical_sha256":"c4917d7ee8b35a4c12c8c679b50b031515152d7da55ae1190a1289f4fe1c19b0","source":{"kind":"arxiv","id":"2111.15567","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.15567","created_at":"2026-07-05T09:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"2111.15567v5","created_at":"2026-07-05T09:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.15567","created_at":"2026-07-05T09:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"YSIX27XIWNNE","created_at":"2026-07-05T09:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"YSIX27XIWNNEYEWI","created_at":"2026-07-05T09:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"YSIX27XI","created_at":"2026-07-05T09:05:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:YSIX27XIWNNEYEWIYZ43KCYDCU","target":"record","payload":{"canonical_record":{"source":{"id":"2111.15567","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-11-30T17:00:52Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5f680a1e0ed7d277879b4eaa227d52a12ca3ffa5e8f34fddcbc5a06a9f2bdc00","abstract_canon_sha256":"119ef40962fe34998faf130a3a0ef93ec39aedf5e29c82648c76fde66f008c7a"},"schema_version":"1.0"},"canonical_sha256":"c4917d7ee8b35a4c12c8c679b50b031515152d7da55ae1190a1289f4fe1c19b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:05:07.936198Z","signature_b64":"nxsKhelFbhufBlr+qdQgp7KxtBCw7R4I4K4vp9CdvmuZXGYjp0gOLZlcAmDi+zQgSBWLkgiG7oXzB2SDdi3+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4917d7ee8b35a4c12c8c679b50b031515152d7da55ae1190a1289f4fe1c19b0","last_reissued_at":"2026-07-05T09:05:07.935790Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:05:07.935790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.15567","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7j3YhLy52VjyFKb710SuHb5cM18QVMwQAwPBeshY4jsrbXTJg1Fp1uqgAnWBaPK7IY9FOv4GX6JjYuhNK9j2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T19:51:26.321586Z"},"content_sha256":"f5dc4bcb99d869827310ee754a4a02d34d6b80957ada6238a2ce5551cb463456","schema_version":"1.0","event_id":"sha256:f5dc4bcb99d869827310ee754a4a02d34d6b80957ada6238a2ce5551cb463456"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:YSIX27XIWNNEYEWIYZ43KCYDCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution-free tests of multivariate independence based on center-outward quadrant, Spearman, Kendall, and van der Waerden statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Fang Han, Hongjian Shi, Marc Hallin, Mathias Drton","submitted_at":"2021-11-30T17:00:52Z","abstract_excerpt":"Due to the lack of a canonical ordering in ${\\mathbb R}^d$ for $d>1$, defining multivariate generalizations of the classical univariate ranks has been a long-standing open problem in statistics. Optimal transport has been shown to offer a solution in which multivariate ranks are obtained by transporting data points to a grid that approximates a uniform reference measure (Chernozhukov et al., 2017; Hallin, 2017; Hallin et al., 2021), thereby inducing ranks, signs, and a data-driven ordering of ${\\mathbb R}^d$. We take up this new perspective to define and study multivariate analogues of the sig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.15567","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.15567/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZzLhCUhMep7RTbgdSR1pHUxrp14/oLp2oFw6rOtwvEQfNKnm22T/8l+RXs1ZTuzEe6QOXhR/HmHoGEIZBB5RAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T19:51:26.322152Z"},"content_sha256":"9b1ce591dabaa862cab4fb778f498bb14063eb4ba842d7746277c80f126f010a","schema_version":"1.0","event_id":"sha256:9b1ce591dabaa862cab4fb778f498bb14063eb4ba842d7746277c80f126f010a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YSIX27XIWNNEYEWIYZ43KCYDCU/bundle.json","state_url":"https://pith.science/pith/YSIX27XIWNNEYEWIYZ43KCYDCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YSIX27XIWNNEYEWIYZ43KCYDCU/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":"2026-08-03T19:51:26Z","links":{"resolver":"https://pith.science/pith/YSIX27XIWNNEYEWIYZ43KCYDCU","bundle":"https://pith.science/pith/YSIX27XIWNNEYEWIYZ43KCYDCU/bundle.json","state":"https://pith.science/pith/YSIX27XIWNNEYEWIYZ43KCYDCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YSIX27XIWNNEYEWIYZ43KCYDCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YSIX27XIWNNEYEWIYZ43KCYDCU","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":"119ef40962fe34998faf130a3a0ef93ec39aedf5e29c82648c76fde66f008c7a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-11-30T17:00:52Z","title_canon_sha256":"5f680a1e0ed7d277879b4eaa227d52a12ca3ffa5e8f34fddcbc5a06a9f2bdc00"},"schema_version":"1.0","source":{"id":"2111.15567","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.15567","created_at":"2026-07-05T09:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"2111.15567v5","created_at":"2026-07-05T09:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.15567","created_at":"2026-07-05T09:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"YSIX27XIWNNE","created_at":"2026-07-05T09:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"YSIX27XIWNNEYEWI","created_at":"2026-07-05T09:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"YSIX27XI","created_at":"2026-07-05T09:05:07Z"}],"graph_snapshots":[{"event_id":"sha256:9b1ce591dabaa862cab4fb778f498bb14063eb4ba842d7746277c80f126f010a","target":"graph","created_at":"2026-07-05T09:05:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.15567/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Due to the lack of a canonical ordering in ${\\mathbb R}^d$ for $d>1$, defining multivariate generalizations of the classical univariate ranks has been a long-standing open problem in statistics. Optimal transport has been shown to offer a solution in which multivariate ranks are obtained by transporting data points to a grid that approximates a uniform reference measure (Chernozhukov et al., 2017; Hallin, 2017; Hallin et al., 2021), thereby inducing ranks, signs, and a data-driven ordering of ${\\mathbb R}^d$. We take up this new perspective to define and study multivariate analogues of the sig","authors_text":"Fang Han, Hongjian Shi, Marc Hallin, Mathias Drton","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-11-30T17:00:52Z","title":"Distribution-free tests of multivariate independence based on center-outward quadrant, Spearman, Kendall, and van der Waerden statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.15567","kind":"arxiv","version":5},"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:f5dc4bcb99d869827310ee754a4a02d34d6b80957ada6238a2ce5551cb463456","target":"record","created_at":"2026-07-05T09:05:07Z","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":"119ef40962fe34998faf130a3a0ef93ec39aedf5e29c82648c76fde66f008c7a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-11-30T17:00:52Z","title_canon_sha256":"5f680a1e0ed7d277879b4eaa227d52a12ca3ffa5e8f34fddcbc5a06a9f2bdc00"},"schema_version":"1.0","source":{"id":"2111.15567","kind":"arxiv","version":5}},"canonical_sha256":"c4917d7ee8b35a4c12c8c679b50b031515152d7da55ae1190a1289f4fe1c19b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4917d7ee8b35a4c12c8c679b50b031515152d7da55ae1190a1289f4fe1c19b0","first_computed_at":"2026-07-05T09:05:07.935790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:05:07.935790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nxsKhelFbhufBlr+qdQgp7KxtBCw7R4I4K4vp9CdvmuZXGYjp0gOLZlcAmDi+zQgSBWLkgiG7oXzB2SDdi3+DA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:05:07.936198Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.15567","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5dc4bcb99d869827310ee754a4a02d34d6b80957ada6238a2ce5551cb463456","sha256:9b1ce591dabaa862cab4fb778f498bb14063eb4ba842d7746277c80f126f010a"],"state_sha256":"3b1961cdd4ee1e54a011a15304d698fac55b6f5c1dd0be5cce2d71ebd7a84701"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8c4ad8Ee7Y1dvV+smmKpg+4ZTiVvzYDGl31fpeVpnl25bld2Nv+zhFtH8/yUeaEgrjlc0wjWKZmMVB6LGAQSAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T19:51:26.326116Z","bundle_sha256":"879c367186b08eb84a9e5d8eb3f413db7d56de2e959e8a4439ad5b505de94d66"}}