The even-link image conjecture for the 3d quantum trace

Assume that $Y=S^3\setminus\mathcal{K}$ is an ideally triangulated knot complement. A link $L\subset S^3\setminus\mathcal{K}$ is even if it represents the zero homology class in

$$H_1(S^3\setminus\mathcal{K},\mathbb{Z}_2)\cong\mathbb{Z}_2.$$

Let $\operatorname{Tr}_{\mathcal{T}}$ be the 3d quantum trace map and let $\iota: \operatorname{QGM}_{\mathcal{T}}(Y)\to\operatorname{SQGM}_{\mathcal{T}}(Y)$ be the natural homomorphism. Even-link image conjecture. The image of an even link under $\operatorname{Tr}_{\mathcal{T}}$ is contained in

$$\iota\bigl(\operatorname{QGM}_{\mathcal{T}}(Y)\bigr)\subset\operatorname{SQGM}_{\mathcal{T}}(Y).$$

This predicts that quantum traces of even links lie in the unsquared quantum gluing module inside the squared one; the source gives no resolution.