{"paper":{"title":"A Generalization of a Classical Geometric Extremum Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.MG","authors_text":"Nikolai Nikolov, Oleg Mushkarov, Petar Kenderov","submitted_at":"2025-06-08T18:26:00Z","abstract_excerpt":"Let $\\partial \\,\\mathcal{C}$ be the boundary of a compact convex body $\\mathcal{C}$ in $\\mathbb{R}^n,\\, n\\geq 2$, and $O$ be an interior point of $\\mathcal C$. Every straight line $l$ containing $O$ cuts from $\\mathcal{C}$ a segment $[AB]$ with end-points on $\\partial \\,\\mathcal{C}$. It is shown that if $[AB]$ is the shortest such segment, then $\\partial \\,\\mathcal{C}$ is smooth at the points $A$ and $ B$ (i.e. at both of them there is only one supporting hyperplane for $\\mathcal{C}$) and, something more, the normals to the unique supporting hyperplanes at the points $A$ and $B$ intersect at a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07252","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/2506.07252/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"}