{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NQG22UZQY5EHHPN2EQC5BGQZO4","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":"41c7bc884d7dba9eddd2bfc4c5939bdf15a7784003308f6ed2491f0f4ec33e62","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-07T18:42:37Z","title_canon_sha256":"de15448f66f1a5191820969b1e0c663e65105177232d0e7c08b334fd0bff84eb"},"schema_version":"1.0","source":{"id":"1610.02368","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02368","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02368v2","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02368","created_at":"2026-05-17T23:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"NQG22UZQY5EH","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NQG22UZQY5EHHPN2","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NQG22UZQ","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:7f3214851c822ed3c37be7f9042d71afd879e8ff759994ac256091fce8168cfb","target":"graph","created_at":"2026-05-17T23:59:26Z","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":"The theory of equidistribution is about hundred years old, and has been developed primarily by number theorists and theoretical computer scientists. A motivated uninitiated peer could encounter difficulties perusing the literature, due to various synonyms and polysemes used by different schools. One purpose of this note is to provide a short introduction for probabilists. We proceed by recalling a perspective originating in a work of the second author from 2002. Using it, various new examples of completely uniformly distributed (mod 1) sequences, in the \"metric\" (meaning almost sure stochastic","authors_text":"Ned\\v{z}ad Limi\\'c, Vlada Limic","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-07T18:42:37Z","title":"Equidistribution, Uniform distribution: a probabilist's perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02368","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:d5310de985171a305041f3f5d72a9bd4255afd6d00872ea8f432f84c31893ede","target":"record","created_at":"2026-05-17T23:59:26Z","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":"41c7bc884d7dba9eddd2bfc4c5939bdf15a7784003308f6ed2491f0f4ec33e62","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-07T18:42:37Z","title_canon_sha256":"de15448f66f1a5191820969b1e0c663e65105177232d0e7c08b334fd0bff84eb"},"schema_version":"1.0","source":{"id":"1610.02368","kind":"arxiv","version":2}},"canonical_sha256":"6c0dad5330c74873bdba2405d09a197739344861b685f2a63677d8e8d63a4e54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c0dad5330c74873bdba2405d09a197739344861b685f2a63677d8e8d63a4e54","first_computed_at":"2026-05-17T23:59:26.688516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:26.688516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZTghEg6bA62HNLKAV8ER0C1APaZ0p3d+q2dUrYmQEjJE6EIsC4xjnIxqFXpV5GTASVClmy9KDeU2ZA3VOV2FDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:26.689108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02368","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5310de985171a305041f3f5d72a9bd4255afd6d00872ea8f432f84c31893ede","sha256:7f3214851c822ed3c37be7f9042d71afd879e8ff759994ac256091fce8168cfb"],"state_sha256":"205641f088d0c3835380395d6ca833c49b2a72e0013d397c957dd9dfa6f89cd9"}