Non-commutativity and linguization of Oshida-Rule

Let $A$ be the honest matrix associated with $m\in\mathbb{Z}_{>1}$, and let the identity labelled Oshida-Rule Before be

$$h'\circ h\circ\underbrace{f_1\circ\cdots\circ f_1}_{2m-1}(e)=\underbrace{H_{245}\circ\cdots\circ H_{245}}_{2m-1}\circ h'\circ h(e).$$

Non-commutativity and linguization of Oshida-Rule. It is not possible to prove from the supplied formulation that this identity holds using matrices $A$; equivalently, it is not possible to prove from these matrices that $H_{245}$ can be constructed using $A$.

This is presented as a limitation of the matrix formulation rather than as an asserted mathematical equality or inequality. The source does not state whether the issue has been resolved.