 Strict ordering threshold for SLE boundary swallowing

For $\kappa \ge 8$, almost surely the positive-boundary swallowing times satisfy $T(x)<T(y)$ simultaneously for every $0<x<y$. The SLE two-boundary-point ratio diffusion has unbounded scale, ruling out escape before hitting $1$. For $4<\kappa <8$, its total scale $S_{\kappa }$ is finite, and the simultaneous-swallowing probability is $s_{\kappa }(y/(y-x))/S_{\kappa }$. At $\kappa =4$, fixed positive points have infinite swallowing times.