{"paper":{"title":"The diameter function is a topological Morse function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bhola Nath Saha, Ingrid Irmer","submitted_at":"2026-06-19T10:14:46Z","abstract_excerpt":"Schmutz Schaller developed techniques for studying Teichm\\\"uller space using the systole function. These were presented in \\cite{SchmutzMorse}, \\cite{SchmutzVoronoi} as a hyperbolic analogue of Voronoi's theory of quadratic forms in the theory of Euclidean lattice packings and coverings \\cite{VoronoiPDQF}. It is known that the packing density function on Euclidean space is a topological Morse function, \\cite{TMFAsh}, and the same is true of the systole function on Teichm\\\"uller space, \\cite{Akrout}, \\cite{SchmutzMorse}. The study of hyperbolic packing and covering problems is technical, for ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21291","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/2606.21291/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"}