{"paper":{"title":"Finite asymptotic clusters of metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Oleksiy Dovgoshey, Viktoriia Bilet","submitted_at":"2018-01-02T16:42:53Z","abstract_excerpt":"Let $(X, d)$ be an unbounded metric space and let $\\tilde r=(r_n)_{n\\in\\mathbb N}$ be a sequence of positive real numbers tending to infinity. A pretangent space $\\Omega_{\\infty, \\tilde r}^{X}$ to $(X, d)$ at infinity is a limit of the rescaling sequence $\\left(X, \\frac{1}{r_n}d\\right).$ The set of all pretangent spaces $\\Omega_{\\infty, \\tilde r}^{X}$ is called an asymptotic cluster of pretangent spaces. Such a cluster can be considered as a weighted graph $(G_{X, \\tilde r}, \\rho_{X})$ whose maximal cliques coincide with $\\Omega_{\\infty, \\tilde r}^{X}$ and the weight $\\rho_{X}$ is defined by m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01014","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"}