{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R37RWPCZWEOWBJ3RAZ5ETP5QQH","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":"f4acce3edf96b01c80889e0b151523097530184f65f237ec2073bce9c11d2133","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-30T10:55:54Z","title_canon_sha256":"22c30921e2bf13d559a5a61597a6287d112188c52540b71a8ebc70aebe479f4b"},"schema_version":"1.0","source":{"id":"1708.09211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09211","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09211v1","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09211","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"pith_short_12","alias_value":"R37RWPCZWEOW","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R37RWPCZWEOWBJ3R","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R37RWPCZ","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:fc7aab85a10c16842df498be579ac42ab528e51c5c9001cd73b98349001f902f","target":"graph","created_at":"2026-05-18T00:36:20Z","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 give a simple conceptual proof of the consistency of a test for multivariate uniformity in a bounded set $K \\subset \\mathbb{R}^d$ that is based on the maximal spacing generated by i.i.d. points $X_1, \\ldots,X_n$ in $K$, i.e., the volume of the largest convex set of a given shape that is contained in $K$ and avoids each of these points. Since asymptotic results for the case $d > 1$ are only availabe under uniformity, a key element of the proof is a suitable coupling.","authors_text":"Norbert Henze","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-30T10:55:54Z","title":"On the consistency of the spacings test for multivariate uniformity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09211","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":"sha256:0d57fc561a75ba347fe398c95d59feb55b62089fb1ada0d319c69c04f27d0ca1","target":"record","created_at":"2026-05-18T00:36:20Z","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":"f4acce3edf96b01c80889e0b151523097530184f65f237ec2073bce9c11d2133","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-30T10:55:54Z","title_canon_sha256":"22c30921e2bf13d559a5a61597a6287d112188c52540b71a8ebc70aebe479f4b"},"schema_version":"1.0","source":{"id":"1708.09211","kind":"arxiv","version":1}},"canonical_sha256":"8eff1b3c59b11d60a771067a49bfb081fd5808048a166b68d37ef8effefbee17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8eff1b3c59b11d60a771067a49bfb081fd5808048a166b68d37ef8effefbee17","first_computed_at":"2026-05-18T00:36:20.611756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:20.611756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+xpY3FvxZh5YD93NYfdoQO1WnLmfig4+10J6P2KeB6laQwvOBpleh6hWiWHnzP+Kc/TMKPQvs3oNZg1UnLZ8BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:20.612401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d57fc561a75ba347fe398c95d59feb55b62089fb1ada0d319c69c04f27d0ca1","sha256:fc7aab85a10c16842df498be579ac42ab528e51c5c9001cd73b98349001f902f"],"state_sha256":"deb10aa7cc5f3bbcc2d5a1b77607e1da4e70ed628e88de8a39591a28bd14a8bf"}