Strong free product property conjecture for non-Dynkin quivers

Let $Q$ be a connected, non-Dynkin quiver. Let $L_Q$ be the localized path algebra of the doubled quiver, let $r$ be the multiplicative preprojective relation, and let $B=kQ_0[t,(q+t)^{-1}]$. Let $\sigma'$ be the map determined by the relevant section $\sigma$ of the quotient map.

Strong free product property conjecture. The map $\sigma'$ is a linear isomorphism, equivalently $(L_Q,r,\sigma,kQ_0[t,(t+q)^{-1}])$ satisfies the strong free product property.

The strong free product property would imply both the 2-Calabi–Yau property and formality conjectures for connected non-Dynkin quivers. It is therefore a more general algebraic statement that packages the required normal-form and resolution properties.