{"paper":{"title":"A Large-Diameter Fundamental-Gap Lower Bound for Horoconvex Domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DG","authors_text":"Guofang Wei, John Ennis, Xianzhe Dai, Xuan Hien Nguyen","submitted_at":"2026-06-10T23:20:31Z","abstract_excerpt":"We prove a large-diameter fundamental-gap lower bound for compact horoconvex\n  domains in real hyperbolic space of curvature \\(-1\\). The geometric part\n  reduces large horoconvex domains to a fixed-width radial-height problem in all\n  dimensions. The analytic part proves the needed radial-height theorem by\n  comparing the low-energy Dirichlet form with a limiting angular operator on the\n  sphere, while the radial complement is separated by a one-dimensional branch\n  gap and endpoint Green estimates. The result gives the polynomial \\(D^{-3}\\)\n  scale matching the Nguyen--Stancu--Wei large-diame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12745","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/2606.12745/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"}