Polynomial randomness implies uniform distribution for polynomial-time integer sequences

Let $(a_i)_{i\in\mathbb{N}}$ be a sequence of distinct integers such that the function mapping the unary input $1^j$ to $a_j$ is polynomial-time computable. For a real $y$, write $\operatorname{frac}(a_i y)$ for the fractional part of $a_i y$. Uniform-distribution conjecture. For every polynomially random real $y$, the sequence

$$\bigl(\operatorname{frac}(a_i y)\bigr)_{i\in\mathbb{N}}$$

is uniformly distributed in $[0,1]$. This is a proposed algorithmic-randomness strengthening of Weyl-type uniform-distribution results; the source presents it as a conjectural statement, and its resolution is not supplied.