= Fixed-interior-point avoidance of SLE4
{title2=$\mathbb P(T_z=\infty)=1$}
Every fixed $z\in\mathbb H$ has infinite <interior-point swallowing time for a Loewner chain> under <Schramm–Loewner evolution> at $\kappa=4$. The centered flow is bounded on any finite horizon, making $\log|Z_t|$ bounded above. The <one-sided bound criterion for a martingale clock> gives a finite logarithmic limit at any putative finite swallowing time. Thus $|Z_t|$ stays away from zero and the imaginary coordinate remains positive, so the differential equation extends, a contradiction. In particular the trace misses each fixed interior point almost surely.
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