{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YKH5PH2UPPMITDCX2SON3SAXXB","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":"fe494a5e6457e8ca9ae80c43ea2bc22c664c3169672dadd158621255f0260ab0","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-07-03T14:07:03Z","title_canon_sha256":"a17916685f011e8292431b0f5458796a31042987ec29c7df51159e05a8067816"},"schema_version":"1.0","source":{"id":"2507.02640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.02640","created_at":"2026-07-05T11:31:32Z"},{"alias_kind":"arxiv_version","alias_value":"2507.02640v1","created_at":"2026-07-05T11:31:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.02640","created_at":"2026-07-05T11:31:32Z"},{"alias_kind":"pith_short_12","alias_value":"YKH5PH2UPPMI","created_at":"2026-07-05T11:31:32Z"},{"alias_kind":"pith_short_16","alias_value":"YKH5PH2UPPMITDCX","created_at":"2026-07-05T11:31:32Z"},{"alias_kind":"pith_short_8","alias_value":"YKH5PH2U","created_at":"2026-07-05T11:31:32Z"}],"graph_snapshots":[{"event_id":"sha256:6138ae9113edd7fc2c26a0a8f50e45283a09f856dc1096f3523725a033bb7092","target":"graph","created_at":"2026-07-05T11:31:32Z","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/2507.02640/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a two-sample test for large-dimensional covariance matrices in generalized elliptical models. The test statistic is based on a U-statistic estimator of the squared Frobenius norm of the difference between the two population covariance matrices. This statistic was originally introduced by Li and Chen (2012, AoS) for the independent component model. As a key theoretical contribution, we establish a new central limit theorem for the U-statistics under elliptical data, valid under both the null and alternative hypotheses. This result enables asymptotic control of the test level and faci","authors_text":"Nina D\\\"ornemann","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-07-03T14:07:03Z","title":"Two-Sample Covariance Inference in High-Dimensional Elliptical Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.02640","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:cde67124a956bc7948d165eb7d2a3c8ca6790faafb2b6758ce800bdabe45234f","target":"record","created_at":"2026-07-05T11:31:32Z","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":"fe494a5e6457e8ca9ae80c43ea2bc22c664c3169672dadd158621255f0260ab0","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-07-03T14:07:03Z","title_canon_sha256":"a17916685f011e8292431b0f5458796a31042987ec29c7df51159e05a8067816"},"schema_version":"1.0","source":{"id":"2507.02640","kind":"arxiv","version":1}},"canonical_sha256":"c28fd79f547bd8898c57d49cddc817b8422e489855bd5611ce37f77a480a54f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c28fd79f547bd8898c57d49cddc817b8422e489855bd5611ce37f77a480a54f3","first_computed_at":"2026-07-05T11:31:32.220906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:31:32.220906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3yj5pzLoLfBMxe2AsxJzd7i2Bp+5DiA9u0rL6oTJD0i/M5y5u0zBweX+PdpemTmo+HGWOQN/vPyuefm5k7/EDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:31:32.221306Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.02640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cde67124a956bc7948d165eb7d2a3c8ca6790faafb2b6758ce800bdabe45234f","sha256:6138ae9113edd7fc2c26a0a8f50e45283a09f856dc1096f3523725a033bb7092"],"state_sha256":"e2955596c65a0060c963bb37e9e54ab70f97783fee826e2ac718fbb3f77908db"}