Conjectured continuum Kasparov module from the graph sequence

Let $M$ be the underlying 3-manifold and let $\Omega$ be the infinite system of graphs in $M$. For each $n$, let $(\mathbb{X}_n(M),H_{\phi_n^t},D_n)$ be the associated unbounded Kasparov bimodule, and let $\mathbb{X}(M)$ and $H_{\phi^t}$ denote their continuum limits.

Continuum Kasparov-module conjecture. The infinite sequence

$$\\{(\mathbb{X}_n(M),H_{\phi_n^t},D_n)\\}$$

of Kasparov modules assigned to $\Omega$ gives a Kasparov module

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

This is intended to provide the continuum limit of the finite-graph Kasparov modules. The source identifies the existence of the limiting operator and its spectral behavior as unresolved.