Brownian rough path small-ball positivity ($\mathbb{P}(d_p(\mathbf{B},e)<\epsilon )>0$)

For every $2<p<3$ and every positive radius, the canonical Brownian enhancement has positive probability of lying in the displayed rough path metric ball. This controls both displacement and area. Together with Cameron-Martin quasi-invariance of enhanced Brownian motion, it puts every lifted Cameron-Martin control in the support of enhanced Brownian motion.