{"paper":{"title":"On three early papers by Herbert Busemann","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.HO"],"primary_cat":"math.MG","authors_text":"Athanase Papadopoulos (IRMA), Marc Troyanov","submitted_at":"2016-10-24T11:42:52Z","abstract_excerpt":"This paper is a commentary and a reading guide to three papers by Herbert Busemann,   \\\"Uber die Geometrien, in denen die  \"Kreise mit unendlichem Radius\"   die k\\\"urzesten Linien sind.\"    (On the geometries where circles of infinite radius are the shortest lines) (1932), \"Paschsches Axiom und Zweidimensionalit\\\"at,\"  (Pasch's Axiom and Two--Dimensionality) (1933) and \"\\\"Uber  R\\\"aume mit konvexen Kugeln und Parallelenaxiom (On spaces with convex spheres and the parallel postulate) (1933). These are the first papers that Busemann wrote on the foundations of geometry and the axiomatic characte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07372","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"}