The dimension conjecture for the twisted Zhu algebra of the supertriplet algebra

Let $m\in\mathbb{N}$ and let $A_{\sigma}(\mathcal{SW}(m))$ denote the $\sigma$-twisted Zhu algebra of the supertriplet vertex operator superalgebra.

Twisted Zhu-algebra dimension conjecture.

$$\dim A_{\sigma}(\mathcal{SW}(m))=12m+8.$$

The source establishes only the lower bound $\dim A_{\sigma}(\mathcal{SW}(m))\geq 10m+8$ and motivates the conjecture by the expected existence of logarithmic modules, so the equality remains unresolved.