Finite-dimensionality conjecture for the classical F4(d) family

Let $F4(d)$ be the symmetric ribbon category generated by a trivalent vertex subject to the defining $F4(d)$ relations, and let $\operatorname{Hom}$ denote a morphism space in this category. Finite-dimensionality conjecture for $F4(d)$. For every parameter $d$, $F4(d)$ has finite-dimensional $\operatorname{Hom}$ spaces. The source describes this as a sufficiency conjecture and notes partial evidence, but the supplied statement does not specify a restriction on $d$.