{"paper":{"title":"The sharp exponent for the minimal distance problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG","math.NT"],"primary_cat":"math.CO","authors_text":"Cosmin Pohoata","submitted_at":"2026-07-22T17:58:33Z","abstract_excerpt":"We show that for every fixed $\\varepsilon>0$, there exist arbitrarily large families of point-line pairs $(x_1,\\ell_1),\\ldots,(x_n,\\ell_n)$ in $[0,1]^2$, with $x_i \\in \\ell_i$ for all $i$, and such that $\\operatorname{dist}(x_i,\\ell_j)\\ge n^{-2/3-\\varepsilon}$ for all $i \\neq j$. Combined with a previous result of Cohen, the author, and Zakharov, this solves the minimal distance problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20422","kind":"arxiv","version":1},"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/2607.20422/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"}