{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VZVLSVG2KEB3T6YPKFJXP5N5Q3","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":"f3f99676faa1a8ee0638b65ff8448844e169e5c44b0da483a4ba6188c64fd0f7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-06-28T19:39:38Z","title_canon_sha256":"0e17fa05280e65ea6d4bd6a45c604de248d7d70da29155a92445602dacd724ff"},"schema_version":"1.0","source":{"id":"1406.7434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7434","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7434v1","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7434","created_at":"2026-05-18T02:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"VZVLSVG2KEB3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VZVLSVG2KEB3T6YP","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VZVLSVG2","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:e8c539eb109dfa3ac6f0f6a6d84747b6a35c215a1547fc7e3be2b509fc926c9f","target":"graph","created_at":"2026-05-18T02:48:45Z","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":"Recently, several strong limit theorems for the oscillation moduli of the empirical process have been given in the iid-case. We show that, with very slight differences, those strong results are also obtained for some representation of the reduced empirical process based on the (non-overlapping) k-spacings generated by a sequence of independent random variables (rv's) uniformly distributed on $(0,1)$. This yields weak limits for the mentioned process. Our study includes the case where the step k is unbounded. The results are mainly derived from several properties concerning the increments of ga","authors_text":"Gane Samb Lo","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-06-28T19:39:38Z","title":"Strong limits related to the oscillation modulus of the empirical process based on the k-spacing process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7434","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":"sha256:9fe1b0f2acf6eff3e4b7c9b66166e50fb15a7382068b18559529d4b419ebf99d","target":"record","created_at":"2026-05-18T02:48:45Z","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":"f3f99676faa1a8ee0638b65ff8448844e169e5c44b0da483a4ba6188c64fd0f7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-06-28T19:39:38Z","title_canon_sha256":"0e17fa05280e65ea6d4bd6a45c604de248d7d70da29155a92445602dacd724ff"},"schema_version":"1.0","source":{"id":"1406.7434","kind":"arxiv","version":1}},"canonical_sha256":"ae6ab954da5103b9fb0f515377f5bd86ebc8d2a955194b57eae6cfe24a362329","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae6ab954da5103b9fb0f515377f5bd86ebc8d2a955194b57eae6cfe24a362329","first_computed_at":"2026-05-18T02:48:45.326891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:45.326891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dddWqfgRHlDcnFtWUWSfxmGzFV1gL22WNDb66+Vl6s3DjVICeAMmtYgo0/TDrQ0FLN17iY/alHkCoDFsCYFbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:45.327610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fe1b0f2acf6eff3e4b7c9b66166e50fb15a7382068b18559529d4b419ebf99d","sha256:e8c539eb109dfa3ac6f0f6a6d84747b6a35c215a1547fc7e3be2b509fc926c9f"],"state_sha256":"1e85bfee2ce5694ae3c7b77b13d994dad6b963634b9b14e502b66fcb06f25c5b"}