{"paper":{"title":"Improving Kaufman's exceptional set estimate for packing dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Tuomas Orponen","submitted_at":"2016-10-21T11:40:27Z","abstract_excerpt":"Given $0 < s < 1$, I prove that there exists a constant $\\epsilon = \\epsilon(s) > 0$ such that the following holds. Let $K \\subset \\mathbb{R}^{2}$ be a Borel set with $\\mathcal{H}^{1}(K) > 0$, and let $E_{s}(K) \\subset S^{1}$ be the collection of unit vectors $e$ such that $$\\dim_{\\mathrm{p}} \\pi_{e}(K) \\leq s.$$ Then $\\dim_{\\mathrm{H}} E_{s}(K) \\leq s - \\epsilon$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06745","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"}