{"paper":{"title":"Small intersection numbers in the curve graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Samuel J. Taylor, Tarik Aougab","submitted_at":"2013-10-17T14:23:07Z","abstract_excerpt":"Let $S_{g,p}$ denote the genus $g$ orientable surface with $p \\ge 0$ punctures, and let $\\omega(g,p)= 3g+p-4$. We prove the existence of infinitely long geodesic rays $\\left\\{v_{0},v_{1}, v_{2}, ...\\right\\}$ in the curve graph satisfying the following optimal intersection property: for any natural number $k$, the endpoints $v_{i},v_{i+k}$ of any length $k$ subsegment intersect $O(\\omega^{k-2})$ times. By combining this with work of the first author, we answer a question of Dan Margalit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4711","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"}