{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:4LRCEKNR7C5KVA44VLTC3HQWWK","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":"cfb3ed13833d961e35a520de629d62494469b57ecd11e214a1e42226de836d47","cross_cats_sorted":["math.CO","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-08-24T13:24:47Z","title_canon_sha256":"66323c4b6b159b8dccd8938dcd7ad79672adee292933a17d729daeb3465e38f6"},"schema_version":"1.0","source":{"id":"0908.3437","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.3437","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"arxiv_version","alias_value":"0908.3437v2","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3437","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"pith_short_12","alias_value":"4LRCEKNR7C5K","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4LRCEKNR7C5KVA44","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4LRCEKNR","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:f29464f0277e803cb9c7deb97ba4e8ebd4e1a4d162474d90792dffa17863dda4","target":"graph","created_at":"2026-05-18T04:35:14Z","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 study a class of hypothesis testing problems in which, upon observing the realization of an $n$-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether there is a subset of the components belonging to a certain given class of sets whose elements have been ``contaminated,'' that is, have a mean different from zero. We establish some general conditions under which testing is possible and others under which testing is hopeless with a small risk. The combinatorial and geometric structure of the class of sets is s","authors_text":"G\\'abor Lugosi, Louigi Addario-Berry, Luc Devroye, Nicolas Broutin","cross_cats":["math.CO","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-08-24T13:24:47Z","title":"On combinatorial testing problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3437","kind":"arxiv","version":2},"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":"sha256:4544500a5cf4426e2af8dd06b64b68f50590b5943537255cd5fce572f631410a","target":"record","created_at":"2026-05-18T04:35:14Z","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":"cfb3ed13833d961e35a520de629d62494469b57ecd11e214a1e42226de836d47","cross_cats_sorted":["math.CO","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-08-24T13:24:47Z","title_canon_sha256":"66323c4b6b159b8dccd8938dcd7ad79672adee292933a17d729daeb3465e38f6"},"schema_version":"1.0","source":{"id":"0908.3437","kind":"arxiv","version":2}},"canonical_sha256":"e2e22229b1f8baaa839caae62d9e16b2aba79a24bbe655004d212ea07bfc12ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2e22229b1f8baaa839caae62d9e16b2aba79a24bbe655004d212ea07bfc12ff","first_computed_at":"2026-05-18T04:35:14.975123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:14.975123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dZoMkAW6XNXFdqYDcFjiJCQ8mdpHhTkoGL/iSno7jN06nozycFVYVNAvnbe7OZOL7ZPGrnKup89s4QdX65/4DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:14.975577Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.3437","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4544500a5cf4426e2af8dd06b64b68f50590b5943537255cd5fce572f631410a","sha256:f29464f0277e803cb9c7deb97ba4e8ebd4e1a4d162474d90792dffa17863dda4"],"state_sha256":"38e92106c73ab2e538496fcf80747a9f3a3f484c84d1f20e8ef879719cd2b36a"}