Exponent-pair approximation conjecture

Let $r\geq 1$ be real and let an exponent pair $(k,\ell)$ mean an exponent pair in the standard sense. Exponent-pair approximation conjecture. For every real $\varepsilon>0$, there exists an exponent pair $(k,\ell)$ such that

$$\left|\frac{\ell}{k}-r\right|<\varepsilon.$$

In light of the preceding theorem, this would provide exponent pairs arbitrarily close to the ratio required for the paper's estimates and may be of independent interest.