{"paper":{"title":"Categories generated by a trivalent vertex","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.CT"],"primary_cat":"math.QA","authors_text":"Emily Peters, Noah Snyder, Scott Morrison","submitted_at":"2015-01-27T18:51:28Z","abstract_excerpt":"This is the first paper in a general program to automate skein theoretic arguments. In this paper, we study skein theoretic invariants of planar trivalent graphs. Equivalently, we classify trivalent categories, which are nondegenerate pivotal tensor categories over $\\mathbb C$ generated by a symmetric self-dual simple object $X$ and a rotationally invariant morphism $1 \\rightarrow X \\otimes X \\otimes X$. Our main result is that the only trivalent categories with $\\dim \\operatorname{Hom}(1, X^{\\otimes n})$ bounded by $1,0,1,1,4,11,40$ for $0 \\leq n \\leq 6$ are quantum $SO(3)$, quantum $G_2$, a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06869","kind":"arxiv","version":3},"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"}