{"paper":{"title":"Visible parts and lower bounds on point-ray incidences","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.CA","math.MG"],"primary_cat":"math.CO","authors_text":"Alex Rutar, Tuomas Orponen","submitted_at":"2026-06-05T06:43:20Z","abstract_excerpt":"Let $K \\subset \\mathbb{R}^{2}$ be a compact set. For $\\theta \\in S^{1}$, let $\\mathrm{Vis}_{\\theta}(K) \\subset K$ be the visible part of $K$ in direction $\\theta$. We prove that $\\operatorname{dim}_{\\mathrm{H}} \\mathrm{Vis}_{\\theta}(K) \\leq \\tfrac{3}{2}$ for $\\mathcal{H}^{1}$ almost every $\\theta \\in S^{1}$. The previous record was $\\operatorname{dim}_{\\mathrm{H}}\\mathrm{Vis}_{\\theta}(K) \\leq 11/6 \\approx 1.833$, due to D. D\\k{a}browski.\n  Our main tool is a variant of a recent incidence lower bound theorem due to Cohen, Pohoata, and Zakharov where, roughly speaking, lines have been replaced b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06965","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/2606.06965/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"}