Modularity conjecture for q-holonomic modules of proper q-hypergeometric sums

Let a proper $q$-hypergeometric multi-dimensional sum be a proper $q$-hypergeometric sum in multiple variables, and let its associated $q$-holonomic module be the corresponding module of $q$-difference relations. A module is modular if it arises from the modular $q$-difference framework developed in the paper, equivalently if its cocycle data have the required modular transformation properties. Modularity conjecture. Every $q$-holonomic module associated to a proper $q$-hypergeometric multi-dimensional sum is modular. This conjecture proposes that the modular structure exhibited by the examples in the paper extends to all such sums; the supplied text does not state a resolution.