{"paper":{"title":"Delaunay Bifiltrations of Functions on Point Clouds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"cs.CG","authors_text":"\\'Angel Javier Alonso, Michael Kerber, Michael Lesnick, Tung Lam","submitted_at":"2023-10-24T15:07:08Z","abstract_excerpt":"The Delaunay filtration $\\mathcal{D}_{\\bullet}(X)$ of a point cloud $X\\subset \\mathbb{R}^d$ is a central tool of computational topology. Its use is justified by the topological equivalence of $\\mathcal{D}_{\\bullet}(X)$ and the offset (i.e., union-of-balls) filtration of $X$. Given a function $\\gamma: X \\to \\mathbb{R}$, we introduce a Delaunay bifiltration $\\mathcal{DC}_{\\bullet}(\\gamma)$ that satisfies an analogous topological equivalence, ensuring that $\\mathcal{DC}_{\\bullet}(\\gamma)$ topologically encodes the offset filtrations of all sublevel sets of $\\gamma$, as well as the topological rel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.15902","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/2310.15902/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"}