Stability conjecture for higher-arity global dimensions

Let $T$ be a $\Gamma$-semiring and, for each integer $n\geq 3$, let $\mathrm{gldim}^{(n)}_\Gamma(T)$ denote its $n$-ary global dimension. Stability conjecture. For all $n\geq 3$, the global dimension stabilizes:

$$\lim_{n\to\infty} \mathrm{gldim}^{(n)}_\Gamma(T)=\mathrm{gldim}^{(3)}_\Gamma(T).$$

Thus arity $3$ already captures full derived complexity. This conjecture concerns whether higher-arity extensions add no asymptotic global-dimensional complexity; the source provides no evidence that it has been proved or disproved.