{"paper":{"title":"Large Independent Sets in Flag Spheres","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Varun Shah","submitted_at":"2026-06-15T01:54:25Z","abstract_excerpt":"For every $d \\geq 4$, we construct a family of $(d-1)$-dimensional flag simplicial spheres $\\mathcal K_n$ whose graphs contain independent sets of size asymptotically equal to the number of vertices. More precisely, we prove that for sufficiently large $n$, $$ \\alpha(G(\\mathcal K_n)) \\geq f_0(\\mathcal K_n) - \\frac{C\\,f_0(\\mathcal K_n)}{\\left(\\log f_0(\\mathcal K_n)\\right)^{\\lfloor d/2 \\rfloor-1}},$$ where $C = C(d) > 0$. This disproves a recent conjecture of Chudnovsky and Nevo."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.16109","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/2606.16109/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"}