= SLE4 angle martingale
{c}
{title2=$\theta_t=\arg(g_t(z)-U_t)$}
For a fixed <interior> point and parameter four, the <SLE angle process> has zero drift and satisfies $\theta_t=\arg z+2\int_0^tY_s|Z_s|^{-2}\,dB_s$. Its values in $(0,\pi)$ make this continuous <local martingale> a true bounded <martingale>. The identity $\log(\Upsilon_t/\Upsilon_0)=-[\theta]_t$, together with the <Dambis-Dubins-Schwarz theorem>, prevents its <Loewner conformal radius> from vanishing at a finite lifetime. Since the parameter-four trace is simple and does not meet the real <boundary> at positive times, finite swallowing would require a visit to the point and vanishing radius. Thus its <Loewner swallowing time> is infinite almost surely. This gives a global continuous bounded <martingale>, not just one defined before swallowing.
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