{"paper":{"title":"Normalized volume spectra of right-angled hyperbolic polyhedra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"A. Egorov, A. Vesnin","submitted_at":"2026-05-18T15:39:24Z","abstract_excerpt":"Let a three-dimensional hyperbolic polyhedron $\\mathcal P$ have finite volume $\\mathrm{vol}(\\mathcal P)$ and a finite number of vertices $\\mathrm{ver}(\\mathcal P)$. We call its normalized volume the quantity $\\omega(\\mathcal P) = \\mathrm{vol}(\\mathcal P)/ \\mathrm{ver}(\\mathcal P)$. If $\\mathcal{R}$ is some set of hyperbolic polyhedra, then we assign to it the set of normalized volumes $\\Omega (\\mathcal R) = \\{ \\omega(\\mathcal P) \\mid \\mathcal P \\in \\mathcal R \\}$, which we call the spectrum of normalized volumes of the set $\\mathcal R$. In the paper we consider the set $\\mathcal R_{comp}$ of c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18558","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/2605.18558/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.369145Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"30a9a865ff7787699afffd8f0600a7e14d660cb73ded7235425fac950552065c"},"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"}