  We consider the summatory function of the totient function after applications
of a suitable smoothing operator and study the limiting behavior of the
associated error term. Under several conditional assumptions, we show that the
smoothed error term possesses a limiting logarithmic distribution through a
framework consolidated by Akbary--Ng--Shahabi. To obtain this result, we prove
a truncated version of Perron's inversion formula for arbitrary Riesz typical
means. We conclude with a conditional proof that at least two applications of
the smoothing operator are necessary and sufficient to bound the growth of the
error term by $\sqrt{x}$.
