Closure conjecture for multivariate q-holonomic sequences

Let multivariate $q$-holonomic sequences be sequences in several discrete and $q$-variables satisfying the corresponding multivariate $q$-holonomic recurrences. For $\beta$ a complex root of unity and $\boldsymbol{q}\to\boldsymbol{q}^{\boldsymbol{\alpha}}$ a substitution with $\boldsymbol{\alpha}\in\mathbbm Q^s$, the resulting sequences are again multivariate $q$-holonomic.

Closure conjecture. Multivariate $q$-holonomic sequences are closed under twisting by complex roots of unity and under substitutions of the form $q\to q^{\alpha}$ for $\alpha\in\mathbbm Q$.

The statement is presented without proof as a stronger version of the preceding twisting and substitution theorems. Its precise multivariate setting is more involved, and the paper does not give a precise definition of multivariate $q$-holonomicity.