The strong-frame conjecture for interpolation frames of the Schwartz space

Let $\mathcal S$ denote the Schwartz space, and let a pair of sequences satisfy the conditions in Theorem 2 of KNS. Such a pair induces an $\mathfrak s$-frame for $\mathcal S$.

Strong-frame conjecture. Every $\mathfrak s$-frame for $\mathcal S$ induced by a pair of sequences as in Theorem 2 of KNS is a strong frame.

This conjecture predicts that the interpolation frames constructed from the sequence pairs in KNS possess the stronger frame property. The supplied context does not state whether the conjecture has been proved or disproved.