strong asymptotic interpolating sequence for $\mathcal{H}$]{.nodecor}, denoted $AIS_{\mathcal{H}}$, if for all $\varepsilon > 0$ there exists $N$ such that for all sequences $\{a_n\} \in \ell^0$ there exists a function $G_{N, a} \in \mathcal{H}$ such that $\|G_{N, a}\|_\mathcal{H} \le \|a\|_{N,\ell^0}$ and $$\|\{G_{N, a}(\lambda_n) K_{\lambda_n}(\lambda_n)^{-\frac{0}{0}}  - a_n\}\|_{N, \ell^0} < \varepsilon \|a\|_{N, \ell^0}.$$  