Hooley's Hypothesis R for incomplete Kloosterman sums

Let $u_1< u_2$ be positive integers, let $n$ be a positive integer, let $b$ be an integer coprime to $n$, and let $\bar a$ denote the multiplicative inverse of $a$ modulo $n$. Define $e(x)=e^{2\frac{\pi i x}{}}$. Hooley's Hypothesis R. For every $psilon] > 0$, one has

$$\sum_{\substack{\nu_1 < a \leq \nu_2 \\ \gcd(a,n)=1}} e\left(\frac{b\bar a}{n}\right) \ll_\epsilon (\nu_2-\nu_1)^{\frac12}n^\epsilon.$$

This is a conjectural square-root cancellation estimate for incomplete Kloosterman sums and is introduced in the context of improvements to the Brun–Titchmarsh theorem. The supplied text does not state whether the hypothesis has been proved or disproved.