Conjectured semi-finite spectral triple in the continuum limit

Let $M$ be the underlying 3-manifold, let $\mathbb{X}(M)$ and $H_{\phi^t}$ be the continuum limits of the corresponding graph-level structures, and let $D$ be the limiting operator. Let $Cl(T^*\mathcal{A})$ be the Clifford algebra of the cotangent space of the connection space, and let $\mathbf{D}(M)$ be the continuum algebra whose trace is induced by matrix traces on $\mathbf{D}_n(M)$.

Continuum spectral-triple conjecture. The Kasparov module

$$\\{(\mathbb{X}(M),H_{\phi^t},D)\\}$$

is a semi-finite spectral triple with respect to the trace over $Cl(T^*\mathcal{A})$ and the trace over $\mathbf{D}(M)$ induced by matrix traces over $\mathbf{D}_n(M)$.

Together with the preceding conjecture, this would yield the desired semi-finite spectral triple in the continuum limit. The source does not analyze the existence of $D$ or the behavior of its spectrum, so the claim remains open.