{"id":"hexagon/2611.00008","pdf":"https://hexagonmath.org/pdf/2611.00008v1","url":"https://hexagonmath.org/abs/2611.00008v1","tags":["msc:57K10","msc:53A04","msc:49Q10","computer-assisted proof","ropelength","thickness","tight knots","torus knots"],"score":0,"title":"Certified ropelength bounds for torus knots and the tight knot constant","domain":"math.GT","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.GT","summary":"The tight knot constant $\\alpha_0$ is the largest constant with $L(K)\\ge\\alpha_0\\,\\mathrm{Cr}(K)^{3/4}$ for every knot $K$, where $L$ is the ropelength (unit-radius rope) and $\\mathrm{Cr}$ the crossing number. We exhibit an explicit $C^{1,1}$ embedding of the torus knot $T(19,24)$, with $\\mathrm{Cr}=432$, of thickness at least $1$ and length at most $939.984$. Hence $\\alpha_0\\le 9.9200$. The published bound is $10.76$. The proof is computer-assisted: the knot type is certified by an explicit piecewise-linear path of embedded polygons starting from a polygon on a torus, and the thickness by…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}