{"paper":{"title":"Effective Angular Asymptotics and the Sharp $D^{-3}$ Horoconvex Gap Scale","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Sanghyun Park","submitted_at":"2026-06-09T04:43:08Z","abstract_excerpt":"We prove first-band large-diameter asymptotics for the Dirichlet spectrum on horoconvex domains in real hyperbolic space. After Chebyshev centering, a divergent sequence compactifies to a horospherical support-envelope deficit \\[V\\] on \\[\\mathbb S^{n-1}\\]. For graph domains \\[r<R-V(\\theta)\\], the first band satisfies \\[ \\lambda_{j+1}=\\alpha^2+\\frac{\\pi^2}{R^2} +\\frac{2\\pi^2}{R^3}\\bigl(\\eta_j(T_n+V)-b_0\\bigr)+o(R^{-3}), \\qquad j=0,1, \\] where \\[T_n\\] is the nonlocal spherical operator with multiplier \\[\\psi(\\ell+\\alpha)-\\psi(\\alpha)\\]. Consequently the horoconvex fundamental gap has the sharp \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10416","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/2606.10416/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"}