Quantum structure-constant positivity conjecture

Let $\mathbb{I}^q_\Delta$ be the quantum duality map and let $c^q(\ell,\ell';\ell”)$ denote the coefficients in the product expansion of its basis elements from the stated quantum-duality theorem. Quantum structure-constant positivity conjecture. For all relevant $\ell,\ell',\ell”$, the coefficients satisfy

$$c^q(\ell,\ell';\ell”)\in\mathbb{Z}_{\geq0}[q^{\pm1/3}].$$

This is the quantum analogue of structure-constant positivity; the source gives no resolution.