{"paper":{"title":"On the Glide of 3x+1 Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dingyi Pei, Yuyin Yu","submitted_at":"2017-10-04T10:13:42Z","abstract_excerpt":"For any positive integer $n$, define an iterated function $$ f(n)=\\left\\{\\begin{array}{ll} n/2, & \\mbox{$n$ even,} \\\\ 3n+1, & \\mbox{$n$ odd.} \\end{array} \\right. $$ Suppose $k$ (if it exists) is the lowest number such that $f^{k}(n)<n$, and there are $O(n)$ \"multiply by three and add one\" and $E(n)$ \"divide by two\" from $n$ to $f^{k}(n)$, then there must be $$ 2^{E(n)-1}<3^{O(n)}<2^{E(n)}. $$ Our results confirm the conjecture proposed by Terras in 1976."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01525","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}