{"paper":{"title":"Nerve Models of Subdivision Bifiltrations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Kenneth McCabe, Michael Lesnick","submitted_at":"2024-06-11T19:56:51Z","abstract_excerpt":"We study the size of Sheehy's subdivision bifiltrations, up to homotopy. We focus in particular on the subdivision-Rips bifiltration $\\mathcal{SR}(X)$ of a metric space $X$, the only density-sensitive bifiltration on metric spaces known to satisfy a strong robustness property. Given a simplicial filtration $\\mathcal{F}$ with a total of $m$ maximal simplices across all indices, we introduce a nerve-based simplicial model for its subdivision bifiltration $\\mathcal{SF}$ whose $k$-skeleton has size $O(m^{k+1})$. We also show that the $0$-skeleton of any simplicial model of $\\mathcal{SF}$ has size "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07679","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/2406.07679/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"}