{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TP6QDKFK6NJTD4PVEIMXFVJUJ6","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":"546913a309f5b663b13bdbbe080052b158cae83c1c60d9ece28286f3c755d1a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-10T00:00:15Z","title_canon_sha256":"bf021a984ffc397ef1cd17bb0efdae37a43e394249ce3a0ad9071c4737cb38ac"},"schema_version":"1.0","source":{"id":"1806.03559","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03559","created_at":"2026-05-18T00:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03559v2","created_at":"2026-05-18T00:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03559","created_at":"2026-05-18T00:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"TP6QDKFK6NJT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TP6QDKFK6NJTD4PV","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TP6QDKFK","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:98107bf029e58e5d8bfba76ff8e1e59ae95ed29c6557f60746bfb273617853e1","target":"graph","created_at":"2026-05-18T00:09:52Z","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":"It has been conjectured that the sequence $(3/2)^n$ modulo $1$ is uniformly distributed. The distribution of this sequence is signifcant in relation to unsolved problems in number theory including the Collatz conjecture. In this paper, we describe an algorithm to compute $(3/2)^n$ modulo $1$ to $n = 10^8$. We then statistically analyze its distribution. Our results strongly agree with the hypothesis that $(3/2)^n$ modulo 1 is uniformly distributed.","authors_text":"Daniel Taylor-Rodriguez, J.J.P. Veerman, Paula Neeley, Thomas Roth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-10T00:00:15Z","title":"On the Uniformity of $(3/2)^n$ Modulo 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03559","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":"sha256:63cebd7fc311893a331ce4f987065d0647e74ee8eb756143834eda30e7dbaaa4","target":"record","created_at":"2026-05-18T00:09:52Z","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":"546913a309f5b663b13bdbbe080052b158cae83c1c60d9ece28286f3c755d1a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-10T00:00:15Z","title_canon_sha256":"bf021a984ffc397ef1cd17bb0efdae37a43e394249ce3a0ad9071c4737cb38ac"},"schema_version":"1.0","source":{"id":"1806.03559","kind":"arxiv","version":2}},"canonical_sha256":"9bfd01a8aaf35331f1f5221972d5344fac01b0fbc9d8ce9694653b6ef3618a8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bfd01a8aaf35331f1f5221972d5344fac01b0fbc9d8ce9694653b6ef3618a8d","first_computed_at":"2026-05-18T00:09:52.198773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:52.198773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WpX8M5NoWSkS5WzHQSULk3LUF4BVEc/c9MecYBxGY8zHT49qPeaKopfSrpmjyAf2PDcGw1BM2f+EIGlTPfjNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:52.199339Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03559","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63cebd7fc311893a331ce4f987065d0647e74ee8eb756143834eda30e7dbaaa4","sha256:98107bf029e58e5d8bfba76ff8e1e59ae95ed29c6557f60746bfb273617853e1"],"state_sha256":"d6d36930ebd082c93a89ca9617ddc4bbf448e1723eb29b3abfce73ea0e56618c"}