Socle quotient conjecture for Leavitt path algebras of Kronecker squares

Let $Q$ be a quiver, let $\widehat{Q}$ denote its Kronecker square, and let $L_{\mathbb K}(Q)$ be the Leavitt path algebra over a field $\mathbb K$. Let $\overrightarrow{\operatorname{Soc}}(L_{\mathbb K}(\widehat{Q}))$ be the sum of the transfinite socle series, and let $\overrightarrow{\mathop{\rm P}_l}$ be the union of the transfinite sets of point-line vertices. Write $Q\setminus\overrightarrow{\mathop{\rm P}_l}$ for the quiver obtained by removing the hereditary and saturated closure of these vertices. Socle quotient conjecture. There exists a short exact sequence

$$\overrightarrow{\operatorname{Soc}}(L_{\mathbb K}(\widehat{Q}))\hookrightarrow L_{\mathbb K}(\widehat{Q})\twoheadrightarrow L_{\mathbb K}(Q\setminus\overrightarrow{\mathop{\rm P}_l})\otimes_G L_{\mathbb K}(Q\setminus\overrightarrow{\mathop{\rm P}_l}).$$

The conjecture describes the transfinite socle as the kernel of a quotient of the Leavitt path algebra of the Kronecker square. Its finite-quiver specialization is stated separately in the source.