Sorkin's quantum-field singularity conjecture for Morse geometries

Let $\mathcal{M}$ be a compact cobordism of dimension $n$, $h$ a Riemannian metric, $\zeta>1$ a constant, and $f$ a Morse function. Let $M=\mathcal{M}\setminus(\partial\mathcal{M}\cup\{p_i\}_i)$, where the $p_i$ are the critical points of $f$, and let $g=\lVert df\rVert_h^2h-\zeta\,df\otimes df$ be the induced Lorentzian metric on $M$. The pair $(M,g)$ is the Morse spacetime and $(\mathcal{M},h,f,\zeta)$ is a Morse geometry. Sorkin's conjecture. A quantum field propagating on a Morse geometry $(\mathcal{M},h,f,\zeta)$ has an unphysical singular behaviour if and only if the Morse spacetime $(M,g)$ is causally discontinuous. This conjecture connects topology-changing spacetime geometry with the occurrence of infinite energy bursts in quantum field theory. It is stated as remaining open in the paper; its proposed physical interpretation is that causally continuous Morse spacetimes should support well-behaved quantum fields.