{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6PJ7DV4O6SPWVH3GL54YRADUQV","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":"ebefae852a9f542c74a7cf2c23491972d9a576b6e69cab179b903d79c6f2d773","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-02-13T13:15:35Z","title_canon_sha256":"0ca2ff2c94aed5725238e9b4830408d3eb9db58899bcc796f2db03442041e4ff"},"schema_version":"1.0","source":{"id":"1702.03760","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03760","created_at":"2026-05-18T00:07:28Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03760v2","created_at":"2026-05-18T00:07:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03760","created_at":"2026-05-18T00:07:28Z"},{"alias_kind":"pith_short_12","alias_value":"6PJ7DV4O6SPW","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6PJ7DV4O6SPWVH3G","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6PJ7DV4O","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:17612f99a78a2d04664e314700261791a23b3a081e4e72dc6877b07a2b38669f","target":"graph","created_at":"2026-05-18T00:07:28Z","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 composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a convex subset $\\mathcal{C}$ of $\\mathbb{R}^d$. We adopt a minimax point of view and our primary objective is to describe the smallest Euclidean distance between the null and alternative hypotheses such that there is a test with small total error probability. In particular, we focus on the dependence of this distance on the dimension $d$ and the sample size/variance parameter $n$ giving rise to the minimax separation rate. In this paper we discuss lower ","authors_text":"Alexandra Carpentier, Gilles Blanchard, Maurilio Gutzeit","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-02-13T13:15:35Z","title":"Minimax Euclidean Separation Rates for Testing Convex Hypotheses in $\\mathbb{R}^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03760","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":"sha256:319c1a9543d4a921c8e971ce41ab3b225953c9634155cab91e915469085c0173","target":"record","created_at":"2026-05-18T00:07:28Z","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":"ebefae852a9f542c74a7cf2c23491972d9a576b6e69cab179b903d79c6f2d773","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-02-13T13:15:35Z","title_canon_sha256":"0ca2ff2c94aed5725238e9b4830408d3eb9db58899bcc796f2db03442041e4ff"},"schema_version":"1.0","source":{"id":"1702.03760","kind":"arxiv","version":2}},"canonical_sha256":"f3d3f1d78ef49f6a9f665f798880748545e62e29ed18c4412d2ccc1a3692874a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3d3f1d78ef49f6a9f665f798880748545e62e29ed18c4412d2ccc1a3692874a","first_computed_at":"2026-05-18T00:07:28.485464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:28.485464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rj3sKsWjrHS52frTlUCKKH045JxbCNMekVjQX0kN1PyJbh3xoJose7FL8GcO/epq8YAsQskhP7K12JpOiNH8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:28.486099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03760","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:319c1a9543d4a921c8e971ce41ab3b225953c9634155cab91e915469085c0173","sha256:17612f99a78a2d04664e314700261791a23b3a081e4e72dc6877b07a2b38669f"],"state_sha256":"f0b4b2a8d572809040599849227af80728cac479b574d6e794cccfab6d755b42"}