The quantum connection's exponential-type singularity and quasi-unipotent formal monodromy at infinity

Let $M$ be the variety under consideration, let $q$ be the quantum parameter, and let $\nabla_{\partial_q}$ denote the quantum connection in the direction $\partial_q$. At $q=\infty$, consider its formal monodromies after regularization.

Quantum-connection conjecture. (i) $\nabla_{\partial_q}$ has a singularity of unramified exponential type at $q=\infty$. (ii) The regularized formal monodromies at $q=\infty$ are quasi-unipotent, meaning that their eigenvalues are roots of unity.

These assertions describe the formal asymptotic and arithmetic structure of the quantum connection near the irregular singular point $q=\infty$, while ignoring the Stokes phenomenon. The supplied text does not indicate whether either assertion is known or resolved.