Divisor mod-16 equidistribution conjecture for $\Phi_{4p}(2)$

Let $\mathcal{P}_3$ be the prime set used in the paper, let $\Phi_{4p}(2)$ be the cyclotomic value, and let $\omega(N)$ denote the number of distinct prime divisors of $N$. Divisor mod-16 equidistribution conjecture. There exists $c>0$ such that for all sufficiently large odd primes $p\in\mathcal{P}_3$,

$$\#\bigl\{r\mid\Phi_{4p}(2):r\equiv1\pmod{16}\bigr\}\geq c\,\omega\bigl(\Phi_{4p}(2)\bigr),$$

where $\omega(\Phi_{4p}(2))\to\infty$ as $p\to\infty$. This is proposed as a more credible divisor-level target than density estimates for primes in a progression. Its status is unresolved in the source.