Minimal global dimension conjecture for stability conditions on projective space

Let $n\geq 1$, and let $\operatorname{D}^b(\operatorname{Coh}\mathbb{P}^n)$ be the bounded derived category of coherent sheaves on projective $n$-space. Let $\operatorname{Stab}\operatorname{D}^b(\operatorname{Coh}\mathbb{P}^n)$ be its stability-condition space, with global-dimension function $\operatorname{gldim}$. Minimal global dimension conjecture. The minimal value of $\operatorname{gldim}$ on

$$\operatorname{Stab}\operatorname{D}^b(\operatorname{Coh}\mathbb{P}^n)$$

is $n$. The source notes that this holds for $n=1$ by a calculation, but leaves the assertion for general $n$ as a conjecture.