{"paper":{"title":"Edge-regular graphs with non-negative curvature have polynomial growth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Guy Blachar, Herv\\'e Pajot, Justin Salez","submitted_at":"2026-06-09T16:51:46Z","abstract_excerpt":"A long-standing conjecture in the emerging discrete Bakry-\\'Emery theory asserts that bounded-degree graphs satisfying $\\mathrm{CD}(0,\\infty)$ have polynomial growth. In the present paper, we prove this conjecture for all edge-regular graphs, and even obtain a volume doubling estimate with a constant that depends only on the degree. This is made possible thanks to the discovery of a surprising self-improvement phenomenon, which seems of independent interest: any edge-regular graph satisfying $\\mathrm{CD}(\\kappa,\\infty)$ for some $\\kappa\\in\\mathbb R$ must in fact satisfy $\\mathrm{CD}(\\kappa,n)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11094","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/2606.11094/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"}