{"paper":{"title":"Bounds on Gromov Hyperbolicity Constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Domingo Pestana, Jose M. Rodriguez, Veronica Hernandez","submitted_at":"2015-03-04T15:23:27Z","abstract_excerpt":"If $X$ is a geodesic metric space and $x_{1},x_{2},x_{3} \\in X$, a geodesic triangle  $T=\\{x_{1},x_{2},x_{3}\\}$ is the union of the three geodesics $[x_{1}x_{2}]$, $[x_{2}x_{3}]$ and $[x_{3}x_{1}]$ in $X$. The space $X$ is $\\delta$-hyperbolic in the Gromov sense if any side of $T$ is contained in a $\\delta$-neighborhood of the union of the two   other sides, for every geodesic triangle $T$ in $X$.\n  If $X$ is hyperbolic, we denote by  $\\delta(X)$ the sharp hyperbolicity constant of $X$, i.e. $\\delta(X) =\\inf \\{ \\delta\\geq 0:{0.3cm}$ X ${0.2cm}$ $\\text{is} {0.2cm} \\delta \\text{-hyperbolic} \\}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01340","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"}