An Exact Hausdorff Measure as Natural Length for SLE

Dapeng Zhan

Fix $0<\kappa <8$ and put $d=1+\kappa /8$. Recent work by OpenAI identifies an explicit exact Hausdorff gauge \( h_κ(r)=r^d\bigl(\log\log(1/r)\bigr)^{(2-d)/2} \) for sufficiently small $r$ for…