{"paper":{"title":"Consensus Division in an Arbitrary Ratio","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","cs.GT"],"primary_cat":"cs.CC","authors_text":"Jiawei Li, Paul W. Goldberg","submitted_at":"2022-02-13T05:56:30Z","abstract_excerpt":"We consider the problem of partitioning a line segment into two subsets, so that $n$ finite measures all have the same ratio of values for the subsets. Letting $\\alpha\\in[0,1]$ denote the desired ratio, this generalises the PPA-complete consensus-halving problem, in which $\\alpha=\\frac{1}{2}$. Stromquist and Woodall showed that for any $\\alpha$, there exists a solution using $2n$ cuts of the segment. They also showed that if $\\alpha$ is irrational, that upper bound is almost optimal. In this work, we elaborate the bounds for rational values $\\alpha$. For $\\alpha = \\frac{\\ell}{k}$, we show a lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.06949","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.06949/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}