Stolz–Teichner's geometric description of topological modular forms

Let $X$ be a manifold. Write $\mathcal N=(0,1)$ boundary conditions for the $n$th power of the $c=\frac12$ invertible fermionic $(2+1)$-dimensional topological field theory that couple to a background scalar field valued in $X$.

Stolz–Teichner conjecture. The degree-$n$ topological modular forms of $X$ are

$$\mathrm{TMF}^n(X)=\pi_0\left\{\text{$\mathcal N=(0,1)$ boundary conditions for the $n$th power of the $c=\frac12$ invertible fermionic $(2+1)$-dimensional TFT which couple to a background scalar field valued in $X$}\right\}.$$

Here $\pi_0$ denotes connected components of the resulting space of boundary conditions. This is a conjectural geometric description of TMF, relating it to supersymmetric boundary conditions in invertible fermionic field theories; the supplied source gives no evidence that the conjecture has been resolved.