Pairwise coprime CRT modulus candidate-growth conjecture

Let $N$ be the signal length, and let $m_1$, $m_2$, and $m_3$ be pairwise coprime moduli satisfying $m_1,m_2,m_3=\Theta(\sqrt{N})$. For a $k$-sparse signal, apply 3-view CRT gating and denote the resulting candidate set by $\text{candidates}$. Pairwise coprime candidate-growth conjecture. For any such triple of moduli, there exist $k$-sparse signals for which

$$|\text{candidates}|=\omega(k).$$

The claim predicts superlinear candidate growth even when the moduli are pairwise coprime, extending the adversarial phenomenon beyond the divisibility condition used in the preceding construction. The source provides no resolution, so the conjecture remains open.