{"paper":{"title":"On Visibility Problems with an Infinite Discrete, set of Obstacles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.CO"],"primary_cat":"math.MG","authors_text":"Michael Boshernitzan, Yaar Solomon","submitted_at":"2018-05-29T19:31:02Z","abstract_excerpt":"This paper studies visibility problems in Euclidean spaces $\\mathbb{R}^d$ where the obstacles are the points of infinite discrete sets $Y\\subseteq\\mathbb{R}^d$. A point $x\\in\\mathbb{R}^d$ is called $\\varepsilon$-visible for $Y$ (notation: $x\\in\\mathbf{vis}(Y, \\varepsilon))$ if there exists a ray $L\\subseteq\\mathbb{R}^d$ emanating from $x$ such that $||y-z||\\geq\\varepsilon$, for all $y\\in Y\\setminus\\{x\\}$ and $z\\in L$. A point $x\\in\\mathbb{R}^d$ is called visible for $Y$ (notation: $x\\in\\mathbf{vis}(Y))$ if $x\\in\\mathbf{vis}(Y, \\varepsilon))$, for some $\\varepsilon>0$.\\\\ Our main result is the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11679","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":""},"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"}