{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:V36QJHQOZJD7BXAEALJLKLEFI5","short_pith_number":"pith:V36QJHQO","canonical_record":{"source":{"id":"2607.03335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-07-03T13:53:21Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"fec04450044984342cd676903030ad7febdbe8c01532c910570a4dc3e5a2283d","abstract_canon_sha256":"63c206d3eaf279b3c6a7d3d807bd530456182dac8787ad66e554aaaf74ac3736"},"schema_version":"1.0"},"canonical_sha256":"aefd049e0eca47f0dc0402d2b52c854775bfe2385e45d1481b654aca15101d80","source":{"kind":"arxiv","id":"2607.03335","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.03335","created_at":"2026-07-07T02:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.03335v1","created_at":"2026-07-07T02:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03335","created_at":"2026-07-07T02:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"V36QJHQOZJD7","created_at":"2026-07-07T02:17:37Z"},{"alias_kind":"pith_short_16","alias_value":"V36QJHQOZJD7BXAE","created_at":"2026-07-07T02:17:37Z"},{"alias_kind":"pith_short_8","alias_value":"V36QJHQO","created_at":"2026-07-07T02:17:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:V36QJHQOZJD7BXAEALJLKLEFI5","target":"record","payload":{"canonical_record":{"source":{"id":"2607.03335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-07-03T13:53:21Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"fec04450044984342cd676903030ad7febdbe8c01532c910570a4dc3e5a2283d","abstract_canon_sha256":"63c206d3eaf279b3c6a7d3d807bd530456182dac8787ad66e554aaaf74ac3736"},"schema_version":"1.0"},"canonical_sha256":"aefd049e0eca47f0dc0402d2b52c854775bfe2385e45d1481b654aca15101d80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:17:37.925835Z","signature_b64":"9eFIevzAKi+3nUvB+8De11KqqOvF9GQ/S3iOiE0CUkE1szUORqMpuIlahZTrJVSPpHW/C73GCBSL2mMvUyEIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aefd049e0eca47f0dc0402d2b52c854775bfe2385e45d1481b654aca15101d80","last_reissued_at":"2026-07-07T02:17:37.925054Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:17:37.925054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.03335","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":"2026-07-07T02:17:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bfJQT1OUWt1rdl4gw4hGJQuSpt7QHuyLTs6vs7bG/JZgePekdIQv2IlPECOcx57l6lSQz8uaoSwmMYGkOfnwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T00:14:42.154692Z"},"content_sha256":"ab1f99a6da28eb3fa151b56fea9a68629742a7a3b432b9c206dc44b9258c09f3","schema_version":"1.0","event_id":"sha256:ab1f99a6da28eb3fa151b56fea9a68629742a7a3b432b9c206dc44b9258c09f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:V36QJHQOZJD7BXAEALJLKLEFI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A BHEP test for multivariate normality on incomplete data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Daniel Gaigall, Philipp W\\\"ubbolding","submitted_at":"2026-07-03T13:53:21Z","abstract_excerpt":"A BHEP test for the null hypotesis of multivariate normality on the basis of incomplete data is introduced. Estimators for the underlying unknown parameters in this situation are suggested. The test uses characteristic functions and circumvents the problem of singular covariance matrix estimates. As the sample size tends to infinity, an almost sure limit of the test statistic is obtained under the null hypothesis and under alternatives. The convergence in distribution under the null hypothesis is also proved. Critical values can be obtained using a bootstrap procedure. Simulation studies inves"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03335","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.03335/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":"2026-07-07T02:17:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"maIph1nHfRPtst5NCFNyQEnoozNDBK4oxF1qWvuFAx1D74a9dds02RMQc3OibQpzHsXPBldWMWuMyIYYnOIWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T00:14:42.155200Z"},"content_sha256":"7619c87f3ab6e3a025c13d34781740817294de5f8f6689c9a5d871c37af3293d","schema_version":"1.0","event_id":"sha256:7619c87f3ab6e3a025c13d34781740817294de5f8f6689c9a5d871c37af3293d"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:V36QJHQOZJD7BXAEALJLKLEFI5","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s11749-015-0427-4) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Yamada, T., Romer, M. M., & Richards, D. S. P. (2015). Kurtosis tests for multivariate normality with monotone incomplete data.TEST,24(3), 532–557. doi: 10.1007/s11749 -015-0427-4 25 ˇCoupek, P., Doln´ ık, V., Hl´ avka, Z., & Hlubinka, D. (","arxiv_id":"2607.03335","detector":"doi_compliance","evidence":{"ref_index":16,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"Yamada, T., Romer, M. M., & Richards, D. S. P. (2015). Kurtosis tests for multivariate normality with monotone incomplete data.TEST,24(3), 532–557. doi: 10.1007/s11749 -015-0427-4 25 ˇCoupek, P., Doln´ ık, V., Hl´ avka, Z., & Hlubinka, D. (","reconstructed_doi":"10.1007/s11749-015-0427-4"},"severity":"advisory","ref_index":16,"audited_at":"2026-07-12T03:18:38.885286Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s11749-015-0427-4","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"411e5bd7daf0783b468b3003238397f5dab9e0dbb1ac7ff8e5861294a0a5f4a2","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":12446,"payload_sha256":"370692b4a98973d61f47a5eda356b26a6176bc33c0cbe85d966347df12d62e3b","signature_b64":"hzjeoljRR1H2QUXmgiNXhYEFvt07E3GCxT7ZOKAvbOCDXyH2EWQWZDgxQwvXlHTiRWgJ+ho9D5ZYoe1lDV7fBQ==","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":"2026-07-12T03:22:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vhPOqBpTxWJEODdZpEKzBn0YNS0hdFd5XyDSQuPOq+XMFqlLqwa9Ii72JjrFUmPKybyGiu3p28n0EdPhinKQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T00:14:42.157885Z"},"content_sha256":"9b885072aab434aa5976e472c9f05db45a8dea9b458992de9ce2f79910e4992f","schema_version":"1.0","event_id":"sha256:9b885072aab434aa5976e472c9f05db45a8dea9b458992de9ce2f79910e4992f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V36QJHQOZJD7BXAEALJLKLEFI5/bundle.json","state_url":"https://pith.science/pith/V36QJHQOZJD7BXAEALJLKLEFI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V36QJHQOZJD7BXAEALJLKLEFI5/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":"2026-08-07T00:14:42Z","links":{"resolver":"https://pith.science/pith/V36QJHQOZJD7BXAEALJLKLEFI5","bundle":"https://pith.science/pith/V36QJHQOZJD7BXAEALJLKLEFI5/bundle.json","state":"https://pith.science/pith/V36QJHQOZJD7BXAEALJLKLEFI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V36QJHQOZJD7BXAEALJLKLEFI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:V36QJHQOZJD7BXAEALJLKLEFI5","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":"63c206d3eaf279b3c6a7d3d807bd530456182dac8787ad66e554aaaf74ac3736","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-07-03T13:53:21Z","title_canon_sha256":"fec04450044984342cd676903030ad7febdbe8c01532c910570a4dc3e5a2283d"},"schema_version":"1.0","source":{"id":"2607.03335","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.03335","created_at":"2026-07-07T02:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.03335v1","created_at":"2026-07-07T02:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.03335","created_at":"2026-07-07T02:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"V36QJHQOZJD7","created_at":"2026-07-07T02:17:37Z"},{"alias_kind":"pith_short_16","alias_value":"V36QJHQOZJD7BXAE","created_at":"2026-07-07T02:17:37Z"},{"alias_kind":"pith_short_8","alias_value":"V36QJHQO","created_at":"2026-07-07T02:17:37Z"}],"graph_snapshots":[{"event_id":"sha256:7619c87f3ab6e3a025c13d34781740817294de5f8f6689c9a5d871c37af3293d","target":"graph","created_at":"2026-07-07T02:17:37Z","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/2607.03335/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A BHEP test for the null hypotesis of multivariate normality on the basis of incomplete data is introduced. Estimators for the underlying unknown parameters in this situation are suggested. The test uses characteristic functions and circumvents the problem of singular covariance matrix estimates. As the sample size tends to infinity, an almost sure limit of the test statistic is obtained under the null hypothesis and under alternatives. The convergence in distribution under the null hypothesis is also proved. Critical values can be obtained using a bootstrap procedure. Simulation studies inves","authors_text":"Daniel Gaigall, Philipp W\\\"ubbolding","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-07-03T13:53:21Z","title":"A BHEP test for multivariate normality on incomplete data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.03335","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:ab1f99a6da28eb3fa151b56fea9a68629742a7a3b432b9c206dc44b9258c09f3","target":"record","created_at":"2026-07-07T02:17:37Z","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":"63c206d3eaf279b3c6a7d3d807bd530456182dac8787ad66e554aaaf74ac3736","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-07-03T13:53:21Z","title_canon_sha256":"fec04450044984342cd676903030ad7febdbe8c01532c910570a4dc3e5a2283d"},"schema_version":"1.0","source":{"id":"2607.03335","kind":"arxiv","version":1}},"canonical_sha256":"aefd049e0eca47f0dc0402d2b52c854775bfe2385e45d1481b654aca15101d80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aefd049e0eca47f0dc0402d2b52c854775bfe2385e45d1481b654aca15101d80","first_computed_at":"2026-07-07T02:17:37.925054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:17:37.925054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9eFIevzAKi+3nUvB+8De11KqqOvF9GQ/S3iOiE0CUkE1szUORqMpuIlahZTrJVSPpHW/C73GCBSL2mMvUyEIBQ==","signature_status":"signed_v1","signed_at":"2026-07-07T02:17:37.925835Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.03335","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab1f99a6da28eb3fa151b56fea9a68629742a7a3b432b9c206dc44b9258c09f3","sha256:7619c87f3ab6e3a025c13d34781740817294de5f8f6689c9a5d871c37af3293d","sha256:9b885072aab434aa5976e472c9f05db45a8dea9b458992de9ce2f79910e4992f"],"state_sha256":"3469dae8e7b8fa202f9f563027a9c65e3bcb004b74a720d52fb1d82e81b5cb2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2TC4o5jhXn7v7ZsD7Ww+fs01kMpWh4rZ4HYGg9aCm9NCkbdegAoAabNLDwVb4HLDIImMKz8g1FylYb0is7FLCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T00:14:42.160224Z","bundle_sha256":"0db1945ca61f7f1b2ed4980bc09aba26cdda28a8a9dc7519e6f2fa2a8de2ed96"}}