{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UXUES5S4ZXIAD35C7PCTWSAFTC","short_pith_number":"pith:UXUES5S4","canonical_record":{"source":{"id":"2605.17474","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.ST","submitted_at":"2026-05-17T14:22:46Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"8022d6f84bc4fb5b03035f94bea2c9c73cc36d8ea4223e264d6492562fc0e376","abstract_canon_sha256":"3a1270d2dce47b7ecd30ab2d6da3511fecda2e6d5cef3fbec0bd33031b42ec89"},"schema_version":"1.0"},"canonical_sha256":"a5e849765ccdd001efa2fbc53b480598b81351125f863a995857ebfb2ba06283","source":{"kind":"arxiv","id":"2605.17474","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17474","created_at":"2026-05-20T00:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17474v1","created_at":"2026-05-20T00:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17474","created_at":"2026-05-20T00:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"UXUES5S4ZXIA","created_at":"2026-05-20T00:04:40Z"},{"alias_kind":"pith_short_16","alias_value":"UXUES5S4ZXIAD35C","created_at":"2026-05-20T00:04:40Z"},{"alias_kind":"pith_short_8","alias_value":"UXUES5S4","created_at":"2026-05-20T00:04:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UXUES5S4ZXIAD35C7PCTWSAFTC","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17474","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.ST","submitted_at":"2026-05-17T14:22:46Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"8022d6f84bc4fb5b03035f94bea2c9c73cc36d8ea4223e264d6492562fc0e376","abstract_canon_sha256":"3a1270d2dce47b7ecd30ab2d6da3511fecda2e6d5cef3fbec0bd33031b42ec89"},"schema_version":"1.0"},"canonical_sha256":"a5e849765ccdd001efa2fbc53b480598b81351125f863a995857ebfb2ba06283","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:40.879372Z","signature_b64":"J/W6d7t+h0p7GzLwgGzi8VltduLvttb1SCgimruunlCnGZxsdIUxfYx/7gom4RohbIbYywDmm8p7HSrWDzcjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5e849765ccdd001efa2fbc53b480598b81351125f863a995857ebfb2ba06283","last_reissued_at":"2026-05-20T00:04:40.878147Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:40.878147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17474","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":"2026-05-20T00:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6k2TQMQRi66HMM5jVwhmH3+Qt48kkJqZicVOZ+vs0mbtKyeod4y8Vtudbjhy5YT1TMqmq+Yb5MYAPvFMrdlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T01:18:00.493043Z"},"content_sha256":"2d17da38a2e8d8693a53368ee31991bbc64d340bc183eb02a530c777ed918745","schema_version":"1.0","event_id":"sha256:2d17da38a2e8d8693a53368ee31991bbc64d340bc183eb02a530c777ed918745"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UXUES5S4ZXIAD35C7PCTWSAFTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multivariate EDF tests for uniformity, normality,spherical and elliptical symetry, and independence based on a Brownian sheet deconstruction","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"New EDF tests reduce multivariate normality, symmetry, and independence checks to uniformity testing on the unit hypercube via Brownian sheet decomposition.","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Alejandra Caba\\~na, Enrique M. Caba\\~na","submitted_at":"2026-05-17T14:22:46Z","abstract_excerpt":"This paper extends a recently proposed family of EDF-based goodness-of-fit procedures for the hypercube $[0,1]^p$ - the m-test and the s-test - which are based on a unique deconstruction of the $p$-parameter Brownian sheet into independent Gaussian processes.\n  We use the fact that whenever a null hypothesis implies a joint distribution that factorizes into independent continuous components after a suitable mapping, the problem can be reduced to a uniformity test on the hypercube via componentwise probability integral transforms. Specifically, we introduce and analyze new procedures derived fr"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Empirical power comparisons show that these extended procedures are highly competitive with existing methods in the statistical literature, demonstrating particular sensitivity to coordinate-based dependencies and joint dependency structures.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Whenever a null hypothesis implies a joint distribution that factorizes into independent continuous components after a suitable mapping, the problem can be reduced to a uniformity test on the hypercube via componentwise probability integral transforms.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Extends m-test and s-test via Brownian sheet deconstruction to new EDF procedures for uniformity on S^p, multivariate normality, symmetry, and independence, with competitive empirical power.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"New EDF tests reduce multivariate normality, symmetry, and independence checks to uniformity testing on the unit hypercube via Brownian sheet decomposition.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6577ec7ade9d531844717ef2abfb03c2d10e82f5708b17adbdd1b0770b56ab34"},"source":{"id":"2605.17474","kind":"arxiv","version":1},"verdict":{"id":"60ac784c-6f25-4477-83bf-8e1a6d76ae6a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:32:18.682872Z","strongest_claim":"Empirical power comparisons show that these extended procedures are highly competitive with existing methods in the statistical literature, demonstrating particular sensitivity to coordinate-based dependencies and joint dependency structures.","one_line_summary":"Extends m-test and s-test via Brownian sheet deconstruction to new EDF procedures for uniformity on S^p, multivariate normality, symmetry, and independence, with competitive empirical power.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Whenever a null hypothesis implies a joint distribution that factorizes into independent continuous components after a suitable mapping, the problem can be reduced to a uniformity test on the hypercube via componentwise probability integral transforms.","pith_extraction_headline":"New EDF tests reduce multivariate normality, symmetry, and independence checks to uniformity testing on the unit hypercube via Brownian sheet decomposition."},"integrity":{"clean":false,"summary":{"advisory":0,"critical":1,"by_detector":{"doi_compliance":{"total":1,"advisory":0,"critical":1,"informational":0}},"informational":0},"endpoint":"/pith/2605.17474/integrity.json","findings":[{"note":"Identifier '10.1137/1.9781611970568' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","detector":"doi_compliance","severity":"critical","ref_index":3,"audited_at":"2026-05-19T22:41:24.036621Z","detected_doi":"10.1137/1.9781611970568","finding_type":"unresolvable_identifier","verdict_class":"cross_source","detected_arxiv_id":null}],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.541345Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:41:24.036621Z","status":"completed","version":"1.0.0","findings_count":1},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.694765Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.652220Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"881726d5c7d69febcee18b39676d3225c884acf779cb57eb4ab857c03cf60f13"},"references":{"count":22,"sample":[{"doi":"","year":null,"title":"A. Caba˜ na, E. M. Caba˜ na, Brownian sheet and uniformity tests on the hypercube, to appear in Statistica.arXiv:2509.06134. URLhttps://arxiv.org/abs/2509.06134","work_id":"7f7a7090-3d4a-40ee-8040-3723b62c02c8","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"A. Caba˜ na, E. M. Caba˜ na, Multivariate tests of uniformity, normality, sym- metry and independence, r package, version 0.2.0. URLhttps://github.com/emcabana/MuniCandS","work_id":"45986a81-d35c-4104-bca8-9661c53c4378","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1137/1.9781611970568","year":1973,"title":"Durbin, Distribution Theory for Tests Based on the Sample Distribu- tion Function, no","work_id":"33b53b88-4d97-4cd1-a19b-c42cc3f31868","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"A. Banerjee, I. S. Dhillon, J. Ghosh, S. Sra, Clustering on the unit hyper- sphere using von mises–fisher distributions, Journal of Machine Learning Research 6 (Sep) (2005) 1345–1382","work_id":"e137a09c-f55e-46d2-9d27-6589827a93e8","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"URLhttps://www.R-project.org/","work_id":"cab6a3a5-e18c-4c4c-a649-2e2ea88596ee","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":22,"snapshot_sha256":"a5cce15933dd65e8e1cb48e3fd35e919d90b7bb2a8113f94c7c3dabe94a3c1bd","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"31c7ac371022ec5f9d73db1a54b46095f8631e7a75b264976858ccb021e4c9f2"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"60ac784c-6f25-4477-83bf-8e1a6d76ae6a"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zrBiKRndrBbfoXyZ1fTaiGVuh9prXo3mzG5dKEifzLOcyS599BzTyMuvP/W2PEnC3H586gGC7k4ansMhyI5bDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T01:18:00.494094Z"},"content_sha256":"482e41f2ee7af83b783ec6004b150442175f607babcbe99928eb9de018962f72","schema_version":"1.0","event_id":"sha256:482e41f2ee7af83b783ec6004b150442175f607babcbe99928eb9de018962f72"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:UXUES5S4ZXIAD35C7PCTWSAFTC","target":"integrity","payload":{"note":"Identifier '10.1137/1.9781611970568' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","snippet":"J. Durbin, Distribution Theory for Tests Based on the Sample Distribu- tion Function, no. 9 in CBMS-NSF Regional Conference Series in Ap- plied Mathematics, Society for Industrial and Applied Mathematics, 1973. doi:10.1137/1.9781611970568","arxiv_id":"2605.17474","detector":"doi_compliance","evidence":{"doi":"10.1137/1.9781611970568","arxiv_id":null,"ref_index":3,"raw_excerpt":"J. Durbin, Distribution Theory for Tests Based on the Sample Distribu- tion Function, no. 9 in CBMS-NSF Regional Conference Series in Ap- plied Mathematics, Society for Industrial and Applied Mathematics, 1973. doi:10.1137/1.9781611970568","verdict_class":"cross_source","checked_sources":["crossref_by_doi","openalex_by_doi","doi_org_head"]},"severity":"critical","ref_index":3,"audited_at":"2026-05-19T22:41:24.036621Z","event_type":"pith.integrity.v1","detected_doi":"10.1137/1.9781611970568","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"unresolvable_identifier","evidence_hash":"ee85cf99611befc42468bec2df708f68fe14fa1fc3dcdb7559bdbdd8b0747116","paper_version":1,"verdict_class":"cross_source","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":3479,"payload_sha256":"b27e0965075601a1a9958a37393d359eccf1c179144029db635a255150b77c7e","signature_b64":"uUIoBUkvVuQIKpefWhdgdcGLdbFM93fGK2per0E4cUWBYQdskUuNJAccwyiD2Qn86fhtIiUN6fviExlC1zlmCg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-19T22:42:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BeJjVcF6Vhn6LNf7IQH3T9t/uf4KHEtuiBh9iSudd/++HkV1fL/2UvgOdRBAa0goBXzkBU8EzalYCx/pdQbeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T01:18:00.495628Z"},"content_sha256":"bab41b95407f1a36d18672362d734f7d8497d281ba73feca7a2adcb6805cda77","schema_version":"1.0","event_id":"sha256:bab41b95407f1a36d18672362d734f7d8497d281ba73feca7a2adcb6805cda77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXUES5S4ZXIAD35C7PCTWSAFTC/bundle.json","state_url":"https://pith.science/pith/UXUES5S4ZXIAD35C7PCTWSAFTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXUES5S4ZXIAD35C7PCTWSAFTC/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":"2026-05-21T01:18:00Z","links":{"resolver":"https://pith.science/pith/UXUES5S4ZXIAD35C7PCTWSAFTC","bundle":"https://pith.science/pith/UXUES5S4ZXIAD35C7PCTWSAFTC/bundle.json","state":"https://pith.science/pith/UXUES5S4ZXIAD35C7PCTWSAFTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXUES5S4ZXIAD35C7PCTWSAFTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UXUES5S4ZXIAD35C7PCTWSAFTC","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3a1270d2dce47b7ecd30ab2d6da3511fecda2e6d5cef3fbec0bd33031b42ec89","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.ST","submitted_at":"2026-05-17T14:22:46Z","title_canon_sha256":"8022d6f84bc4fb5b03035f94bea2c9c73cc36d8ea4223e264d6492562fc0e376"},"schema_version":"1.0","source":{"id":"2605.17474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17474","created_at":"2026-05-20T00:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17474v1","created_at":"2026-05-20T00:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17474","created_at":"2026-05-20T00:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"UXUES5S4ZXIA","created_at":"2026-05-20T00:04:40Z"},{"alias_kind":"pith_short_16","alias_value":"UXUES5S4ZXIAD35C","created_at":"2026-05-20T00:04:40Z"},{"alias_kind":"pith_short_8","alias_value":"UXUES5S4","created_at":"2026-05-20T00:04:40Z"}],"graph_snapshots":[{"event_id":"sha256:482e41f2ee7af83b783ec6004b150442175f607babcbe99928eb9de018962f72","target":"graph","created_at":"2026-05-20T00:04:40Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Empirical power comparisons show that these extended procedures are highly competitive with existing methods in the statistical literature, demonstrating particular sensitivity to coordinate-based dependencies and joint dependency structures."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"Whenever a null hypothesis implies a joint distribution that factorizes into independent continuous components after a suitable mapping, the problem can be reduced to a uniformity test on the hypercube via componentwise probability integral transforms."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Extends m-test and s-test via Brownian sheet deconstruction to new EDF procedures for uniformity on S^p, multivariate normality, symmetry, and independence, with competitive empirical power."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"New EDF tests reduce multivariate normality, symmetry, and independence checks to uniformity testing on the unit hypercube via Brownian sheet decomposition."}],"snapshot_sha256":"6577ec7ade9d531844717ef2abfb03c2d10e82f5708b17adbdd1b0770b56ab34"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"31c7ac371022ec5f9d73db1a54b46095f8631e7a75b264976858ccb021e4c9f2"},"integrity":{"available":true,"clean":false,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.541345Z","status":"completed","version":"1.0.0"},{"findings_count":1,"name":"doi_compliance","ran_at":"2026-05-19T22:41:24.036621Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.694765Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.652220Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.17474/integrity.json","findings":[{"audited_at":"2026-05-19T22:41:24.036621Z","detected_arxiv_id":null,"detected_doi":"10.1137/1.9781611970568","detector":"doi_compliance","finding_type":"unresolvable_identifier","note":"Identifier '10.1137/1.9781611970568' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","ref_index":3,"severity":"critical","verdict_class":"cross_source"}],"snapshot_sha256":"881726d5c7d69febcee18b39676d3225c884acf779cb57eb4ab857c03cf60f13","summary":{"advisory":0,"by_detector":{"doi_compliance":{"advisory":0,"critical":1,"informational":0,"total":1}},"critical":1,"informational":0}},"paper":{"abstract_excerpt":"This paper extends a recently proposed family of EDF-based goodness-of-fit procedures for the hypercube $[0,1]^p$ - the m-test and the s-test - which are based on a unique deconstruction of the $p$-parameter Brownian sheet into independent Gaussian processes.\n  We use the fact that whenever a null hypothesis implies a joint distribution that factorizes into independent continuous components after a suitable mapping, the problem can be reduced to a uniformity test on the hypercube via componentwise probability integral transforms. Specifically, we introduce and analyze new procedures derived fr","authors_text":"Alejandra Caba\\~na, Enrique M. Caba\\~na","cross_cats":["stat.ME","stat.TH"],"headline":"New EDF tests reduce multivariate normality, symmetry, and independence checks to uniformity testing on the unit hypercube via Brownian sheet decomposition.","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.ST","submitted_at":"2026-05-17T14:22:46Z","title":"Multivariate EDF tests for uniformity, normality,spherical and elliptical symetry, and independence based on a Brownian sheet deconstruction"},"references":{"count":22,"internal_anchors":0,"resolved_work":22,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"A. Caba˜ na, E. M. Caba˜ na, Brownian sheet and uniformity tests on the hypercube, to appear in Statistica.arXiv:2509.06134. URLhttps://arxiv.org/abs/2509.06134","work_id":"7f7a7090-3d4a-40ee-8040-3723b62c02c8","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"A. Caba˜ na, E. M. Caba˜ na, Multivariate tests of uniformity, normality, sym- metry and independence, r package, version 0.2.0. URLhttps://github.com/emcabana/MuniCandS","work_id":"45986a81-d35c-4104-bca8-9661c53c4378","year":null},{"cited_arxiv_id":"","doi":"10.1137/1.9781611970568","is_internal_anchor":false,"ref_index":3,"title":"Durbin, Distribution Theory for Tests Based on the Sample Distribu- tion Function, no","work_id":"33b53b88-4d97-4cd1-a19b-c42cc3f31868","year":1973},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"A. Banerjee, I. S. Dhillon, J. Ghosh, S. Sra, Clustering on the unit hyper- sphere using von mises–fisher distributions, Journal of Machine Learning Research 6 (Sep) (2005) 1345–1382","work_id":"e137a09c-f55e-46d2-9d27-6589827a93e8","year":2005},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"URLhttps://www.R-project.org/","work_id":"cab6a3a5-e18c-4c4c-a649-2e2ea88596ee","year":2025}],"snapshot_sha256":"a5cce15933dd65e8e1cb48e3fd35e919d90b7bb2a8113f94c7c3dabe94a3c1bd"},"source":{"id":"2605.17474","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T22:32:18.682872Z","id":"60ac784c-6f25-4477-83bf-8e1a6d76ae6a","model_set":{"reader":"grok-4.3"},"one_line_summary":"Extends m-test and s-test via Brownian sheet deconstruction to new EDF procedures for uniformity on S^p, multivariate normality, symmetry, and independence, with competitive empirical power.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"New EDF tests reduce multivariate normality, symmetry, and independence checks to uniformity testing on the unit hypercube via Brownian sheet decomposition.","strongest_claim":"Empirical power comparisons show that these extended procedures are highly competitive with existing methods in the statistical literature, demonstrating particular sensitivity to coordinate-based dependencies and joint dependency structures.","weakest_assumption":"Whenever a null hypothesis implies a joint distribution that factorizes into independent continuous components after a suitable mapping, the problem can be reduced to a uniformity test on the hypercube via componentwise probability integral transforms."}},"verdict_id":"60ac784c-6f25-4477-83bf-8e1a6d76ae6a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2d17da38a2e8d8693a53368ee31991bbc64d340bc183eb02a530c777ed918745","target":"record","created_at":"2026-05-20T00:04:40Z","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":"3a1270d2dce47b7ecd30ab2d6da3511fecda2e6d5cef3fbec0bd33031b42ec89","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.ST","submitted_at":"2026-05-17T14:22:46Z","title_canon_sha256":"8022d6f84bc4fb5b03035f94bea2c9c73cc36d8ea4223e264d6492562fc0e376"},"schema_version":"1.0","source":{"id":"2605.17474","kind":"arxiv","version":1}},"canonical_sha256":"a5e849765ccdd001efa2fbc53b480598b81351125f863a995857ebfb2ba06283","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5e849765ccdd001efa2fbc53b480598b81351125f863a995857ebfb2ba06283","first_computed_at":"2026-05-20T00:04:40.878147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:40.878147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J/W6d7t+h0p7GzLwgGzi8VltduLvttb1SCgimruunlCnGZxsdIUxfYx/7gom4RohbIbYywDmm8p7HSrWDzcjDg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:40.879372Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bab41b95407f1a36d18672362d734f7d8497d281ba73feca7a2adcb6805cda77","sha256:2d17da38a2e8d8693a53368ee31991bbc64d340bc183eb02a530c777ed918745","sha256:482e41f2ee7af83b783ec6004b150442175f607babcbe99928eb9de018962f72"],"state_sha256":"9277c21b3daa5108beb9c4714e2e59f2f54ca8d16a44fd6ccc5e844fafa479af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y4/rEiVCteEdhrxCWCTV2btwNSlxBRHh8WUljZcIaT2BJ4AB8jbNp9PWNLCVNnGKS90h4B1YN0LED2W4+VHABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T01:18:00.500826Z","bundle_sha256":"7528d48d6a77b7038cae5ff01157cb9921fc2d54fe6e533ca50bdb35124b4516"}}