{"paper":{"title":"An improved bound on the packing dimension of Furstenberg sets in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Tuomas Orponen","submitted_at":"2016-11-29T18:11:03Z","abstract_excerpt":"Let $0 \\leq s \\leq 1$. A set $K \\subset \\mathbb{R}^{2}$ is a Furstenberg $s$-set, if for every unit vector $e \\in S^{1}$, some line $L_{e}$ parallel to $e$ satisfies $$\\dim_{\\mathrm{H}} [K \\cap L_{e}] \\geq s.$$ The Furstenberg set problem, introduced by T. Wolff in 1999, asks for the best lower bound for the dimension of Furstenberg $s$-sets. Wolff proved that $\\dim_{\\mathrm{H}} K \\geq \\max\\{s + 1/2,2s\\}$ and conjectured that $\\dim_{\\mathrm{H}} K \\geq (1 + 3s)/2$. The only known improvement to Wolff's bound is due to Bourgain, who proved in 2003 that $\\dim_{\\mathrm{H}} K \\geq 1 + \\epsilon$ for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09762","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":""},"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"}