Rich restrictions imply non-stable minimality for interval exchange transformations

Let $T_{\boldsymbol{\boldsymbol{\test}}}$ be an interval exchange transformation with permutation $\boldsymbol{\boldsymbol{\test}}$, and let $\boldsymbol{\boldsymbol{\test}}$ be a restriction space. Write $\boldsymbol{\boldsymbol{\test}}$ for the paper's bilinear form associated with the permutation. The space $\boldsymbol{\boldsymbol{\test}}$ is rich with respect to $\boldsymbol{\boldsymbol{\test}}$ when it satisfies the paper's rich-space condition, and $T_{\boldsymbol{\boldsymbol{\test}}}$ is $\boldsymbol{\boldsymbol{\test}}$-stably minimal when minimality persists under perturbations satisfying $\boldsymbol{\boldsymbol{\test}}$.

Rich-restriction instability conjecture. If $\boldsymbol{\boldsymbol{\test}}$ is rich with respect to $\boldsymbol{\boldsymbol{\test}}$ and $T_{\boldsymbol{\boldsymbol{\test}}}$ satisfies all restrictions from $\boldsymbol{\boldsymbol{\test}}$, then $T_{\boldsymbol{\boldsymbol{\test}}}$ is not $\boldsymbol{\boldsymbol{\test}}$-stably minimal.

Together with stability of non-minimality, this would imply that minimal transformations form a nowhere-dense subset of the corresponding restricted parameter space. The supplied text gives no resolution status.