{"paper":{"title":"On Vietoris-Rips complexes of Finite Metric Spaces with Scale $2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Naga Chandra Padmini Nukala, Ziqin Feng","submitted_at":"2023-02-28T15:30:24Z","abstract_excerpt":"We examine the homotopy types of Vietoris-Rips complexes on certain finite metric spaces at scale $2$. We consider the collections of subsets of $[m]=\\{1, 2, \\ldots, m\\}$ equipped with symmetric difference metric $d$, specifically, $\\mathcal{F}^m_n$, $\\mathcal{F}_n^m\\cup \\mathcal{F}^m_{n+1}$, $\\mathcal{F}_n^m\\cup \\mathcal{F}^m_{n+2}$, and $\\mathcal{F}_{\\preceq A}^m$. Here $\\mathcal{F}^m_n$ is the collection of size $n$ subsets of $[m]$ and $\\mathcal{F}_{\\preceq A}^m$ is the collection of subsets $\\preceq A$ where $\\preceq$ is a total order on the collections of subsets of $[m]$ and $A\\subseteq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.14664","kind":"arxiv","version":3},"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/2302.14664/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"}