The syzygy-order formula for big polygon spaces

Let $X_{a,b}(\ell)$ be a big polygon space associated with a length vector $\ell$, let $T$ be the acting torus, and let $\mu(\ell)$ denote the invariant introduced in the paper. The syzygy-order formula asserts

$$\operatorname{syzord}H_T^*(X_{a,b}(\ell))=\mu(\ell)-1.$$

This equality is presented in the source as a result used in the subsequent remark, but the supplied candidate is marked with unknown status and gives no further resolution evidence.