Preservation of cardinal characteristics in shattered Cohen iterations

Let $\mathfrak b$, $\mathfrak d$, and $\mathfrak c$ denote the bounding number, dominating number, and continuum, respectively. Assume

$$\mathfrak b=\aleph_1,\qquad \mathfrak d=\mathfrak c=\nu,$$

and let $\kappa,\lambda$ be regular cardinals with $\aleph_1\leq\kappa<\lambda\leq\nu$. Consider the extension by the shattered iteration of Cohen forcing. Preservation conjecture. In this extension,

$$\mathfrak b=\mathsf{add}(\mathcal M)=\aleph_1$$

and

$$\mathfrak d=\mathsf{cof}(\mathcal M)=\mathfrak c=\nu.$$

The preceding results establish analogous preservation for the null ideal, while the authors state that they believe the corresponding values for the meager ideal and the bounding and dominating numbers are preserved but cannot prove it. The conjecture is open.