Invariance conjecture for sutured embedded contact homology

Let $(M,\Gamma,U(\Gamma),\xi)$ be a sutured contact $3$-manifold with adapted contact form $\alpha$, let $(M^{\ast},\alpha^{\ast})$ be its completion, and let $J$ be an almost complex structure tailored to $(M^{\ast},\alpha^{\ast})$. Write $ECH(M,\Gamma,\alpha,J)$ for the embedded contact homology group of the completion. Invariance conjecture for sutured embedded contact homology. The group $ECH(M,\Gamma,\alpha,J)$ does not depend on the choice of contact form $\alpha$, contact structure $\xi=\operatorname{ker}(\alpha)$, or almost complex structure $J$. The claim is motivated by the invariance of embedded contact homology for closed, oriented $3$-manifolds; the supplied text gives no resolution status.