{"paper":{"title":"Stability of Extended Functional Persistence in Dimensions Zero and One","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Elchanan Solomon","submitted_at":"2018-04-21T23:28:59Z","abstract_excerpt":"The stability result, as stated, is incorrect. In particular, the 1-dimensional extended persistence diagrams of a finely-triangulated simplicial complex X equipped with a continuous real-valued function f, and its one-skeleton graph G (also equipped with f), need not be close. To take an example, let X be a finely-triangulated disc of radius r and let f be the distance-to -the-boundary function, which increases radially from the boundary circle of X and is maximized at the center. The extended persistence diagram of (X,f) contains a point in 1-dimensional persistence of the form (0,r), wherea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09035","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":""},"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"}