Douglas's K-homology fundamental-class conjecture for algebraic sets

Let $V\subseteq\mathbb{C}^{m}$ be an algebraic set intersecting $\partial\mathbb{B}^m$ transversally, and let $I$ be its vanishing ideal. Set $X_I:=V(I)\cap\partial\mathbb{B}^m$. Let $\mathfrak{K}$ be the ideal of compact operators on $I^\perp$, let $\mathfrak{T}_I$ be the unital $C^*$-algebra generated by the compressed multiplication operators and $\mathfrak{K}$, and let $\tau_I$ be the extension class associated with

$$0\rightarrow\mathfrak{K}\hookrightarrow\mathfrak{T}_I\rightarrow C(\sigma_I^e)\rightarrow 0.$$

Douglas's conjecture. Conjecture A holds true, and its induced extension class $\tau_I$ is identified with the fundamental class of $X_I$, namely the extension class induced by the $\operatorname{Spin}^{c}$ Dirac operator associated with the natural Cauchy-Riemann structure of $X_I$.

The conjecture connects essential normality of Drury-Arveson quotient modules with the geometric realization of $K$-homology. The supplied text states the claim in the transversal algebraic-set case but gives no resolution status.