{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5HIGL3XEDFIOLXHIEKSTTSORTJ","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":"a5d411683f5a20cda4c96f63e31bbf4bbd0fe272f7e58f4d36a9f07341393d53","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-02-24T19:48:03Z","title_canon_sha256":"e498f3ab6b12999a3a451bae3450670e804208db8cdd47360064719f182ab49b"},"schema_version":"1.0","source":{"id":"1202.5536","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5536","created_at":"2026-05-18T02:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5536v3","created_at":"2026-05-18T02:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5536","created_at":"2026-05-18T02:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"5HIGL3XEDFIO","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5HIGL3XEDFIOLXHI","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5HIGL3XE","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:c1c32f741e2eda618db8777b1cb664c40783ae0ac268ff28005cca792abae3ec","target":"graph","created_at":"2026-05-18T02:18:52Z","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":"We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a general lower bound applicable to various classes and study the performance of some near-optimal tests. We pay special attention to computational feasibility and construct near-optimal tests that can be computed efficiently. Finally, we apply our results to prove new lower bounds for the clique number of high-dimensional random geometric graphs.","authors_text":"Ery Arias-Castro, G\\'abor Lugosi, S\\'ebastien Bubeck","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-02-24T19:48:03Z","title":"Detecting positive correlations in a multivariate sample"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5536","kind":"arxiv","version":3},"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":"sha256:5279e7fd2c8d1c8e625bb2c6cfbc51e74f48524853f5928d6d97c4611e012a93","target":"record","created_at":"2026-05-18T02:18:52Z","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":"a5d411683f5a20cda4c96f63e31bbf4bbd0fe272f7e58f4d36a9f07341393d53","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-02-24T19:48:03Z","title_canon_sha256":"e498f3ab6b12999a3a451bae3450670e804208db8cdd47360064719f182ab49b"},"schema_version":"1.0","source":{"id":"1202.5536","kind":"arxiv","version":3}},"canonical_sha256":"e9d065eee41950e5dce822a539c9d19a69ba6166a14a1b0d9955e7edcd257e2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9d065eee41950e5dce822a539c9d19a69ba6166a14a1b0d9955e7edcd257e2d","first_computed_at":"2026-05-18T02:18:52.162592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:52.162592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/8xJzMZAlssN/CAqG9kVYBKMr60oAXAiga0+tVNjfASG8G9o+9Veg6kRQ5gSHYnVsAwqy2BNhBdxq37CHfjOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:52.163176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5536","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5279e7fd2c8d1c8e625bb2c6cfbc51e74f48524853f5928d6d97c4611e012a93","sha256:c1c32f741e2eda618db8777b1cb664c40783ae0ac268ff28005cca792abae3ec"],"state_sha256":"47135a187d4fef85b0b04d66f9b3434ec65112ab50857e0b368073d7a47fc035"}