{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OIIV6CYJXQWIZKWN2IQRTWNIC6","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":"b064bfb8e475a5874821f02c2ff49bd743507e0c227427b41cb88bf1342e104b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-10T23:29:41Z","title_canon_sha256":"85bdc80baa709ad8c0bbd5595ba048cb7ca25810e1c9e0b7c2cab7a9e554ec1a"},"schema_version":"1.0","source":{"id":"1410.2927","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2927","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2927v2","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2927","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"OIIV6CYJXQWI","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OIIV6CYJXQWIZKWN","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OIIV6CYJ","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:625c49442048b246169320edb8c5802f956e9b727e51d150f5e1a9d18748f4c4","target":"graph","created_at":"2026-05-18T01:55:33Z","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 study the function M(t,n) = Floor[ 1 / {t^(1/n)} ], where t is a positive real number, Floor[.] and {.} are the floor and fractional part functions, respectively. In a recent article in the Monthly, Nathanson proved that if log(t) is rational, then for all but finitely many positive integers n one has M(t,n) = Floor[ n / log(t) - 1/2 ]. We extend this by showing that, without condition on t, all but a zero-density set of integers n satisfy M(t,n) = Floor[ n / log(t) - 1/2 ]. Using a metric result of Schmidt, we show that almost all t have asymptotically log(t) log(x)/12 exceptional n<x. Usi","authors_text":"Kevin O'Bryant","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-10T23:29:41Z","title":"The sequence of fractional parts of roots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2927","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":"sha256:8866118c7119ba79de9111c6d9f9323686a52e9649cad4e26e50618423683a37","target":"record","created_at":"2026-05-18T01:55:33Z","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":"b064bfb8e475a5874821f02c2ff49bd743507e0c227427b41cb88bf1342e104b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-10T23:29:41Z","title_canon_sha256":"85bdc80baa709ad8c0bbd5595ba048cb7ca25810e1c9e0b7c2cab7a9e554ec1a"},"schema_version":"1.0","source":{"id":"1410.2927","kind":"arxiv","version":2}},"canonical_sha256":"72115f0b09bc2c8caacdd22119d9a817a28d4c1243c1402c5069ac383d38de70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72115f0b09bc2c8caacdd22119d9a817a28d4c1243c1402c5069ac383d38de70","first_computed_at":"2026-05-18T01:55:33.490422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:33.490422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kpKJ8agV6s6hpfn/8M7icJRjORwIVtqbnXk9EnjJM0CHr3xP9L4R6hWnAnxX2Fy8YWyDTbr4NZUtrXYihtc7DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:33.491118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2927","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8866118c7119ba79de9111c6d9f9323686a52e9649cad4e26e50618423683a37","sha256:625c49442048b246169320edb8c5802f956e9b727e51d150f5e1a9d18748f4c4"],"state_sha256":"5500e53a7db459d047a34049a2b8aacc04d6ec51250a3ce9e855cd143610febf"}