The gluing conjecture for non-equidimensional eigenvarieties

For each $a$, let $\mathcal{E}_{a,q}^{q}$, for $q=0,\ldots,a$, be the eigenvarieties constructed over the corresponding weight spaces, and let $\mathcal{W}_a$ be the weight space. Gluing conjecture. For each $a$, the eigenvarieties $\mathcal{E}_{a,q}^{q}$ ($q=0,\ldots,a$) glue to a non-equidimensional eigenvariety $\mathcal{E}_{a}$ over $\mathcal{W}_a$. The proposed gluing would provide a global eigenvariety accommodating the varying parameters $q$ and $s$, while the preceding discussion notes that non-reducedness can prevent the corresponding base changes from being isomorphic.