{"paper":{"title":"Generic Absence of Finite Blocking for Interior Points of Birkhoff Billiards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marlies Gerber, Thomas Dauer","submitted_at":"2015-08-16T19:39:19Z","abstract_excerpt":"Let x and y be points in a billiard table M that is bounded by a curve sigma. We assume that sigma is a simple closed C^r curve with positive curvature, where r is at least 2. A subset B of M\\{x,y} is called a blocking set for the pair (x,y) if every billiard path in M from x to y passes through a point in B. If a finite blocking set exists, the pair (x,y) is called secure in M; if not, it is called insecure. We show that for the generic (in the sense of Baire category) curve sigma, the generic pair of interior points is insecure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03858","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"}