{"paper":{"title":"Accumulation points of the edit distance function","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christopher Cox, Daniel McGinnis, Ryan R. Martin","submitted_at":"2021-07-14T13:50:30Z","abstract_excerpt":"Given a hereditary property $\\mathcal H$ of graphs and some $p\\in[0,1]$, the edit distance function $\\operatorname{ed}_{\\mathcal H}(p)$ is (asymptotically) the maximum proportion of \"edits\" (edge-additions plus edge-deletions) necessary to transform any graph of density $p$ into a member of $\\mathcal H$. For any fixed $p\\in[0,1]$, $\\operatorname{ed}_{\\mathcal H}(p)$ can be computed from an object known as a colored regularity graph (CRG). This paper is concerned with those points $p\\in[0,1]$ for which infinitely many CRGs are required to compute $\\operatorname{ed}_{\\mathcal H}$ on any open int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.06706","kind":"arxiv","version":2},"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/2107.06706/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"}