= Solution
At $\kappa=4$, the <Boundary-point Bessel flow for SLE> has dimension two. Its <scale function of a one-dimensional diffusion> is $s(x)=\log x$, giving
$$
\mathbb P_b(T_\varepsilon<T_R)
=\frac{\log(R/b)}{\log(R/\varepsilon)}\longrightarrow0
\qquad(\varepsilon\downarrow0).
$$
The same bounded-path and countable-union argument as in part (c) excludes a finite zero hit. Hence \b[the critical case belongs to the boundary-avoiding regime]:
$$
\boxed{\mathbb P(\gamma\text{ hits }[b,\infty))=0
\qquad(b>0,\ \kappa=4).}
$$
The countable argument of part (d) gives no visits to any positive real point <almost surely>. By <Reflection invariance of Brownian motion>, reflected <SLE> has the same law, so no negative real point is visited either. Thus the set of real points visited is exactly $\{0\}$. Recurrence of a two-dimensional <Bessel process> near zero does not mean that it hits zero.
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