Undecidability of regular nice labelings for strongly regular event domains

Let $\mathcal D$ be a strongly regular event domain. A regular nice labeling is the labeling property used in Thiagarajan's conjecture. Undecidability conjecture. There does not exist an algorithm that, given $\mathcal D$, determines whether or not $\mathcal D$ admits a regular nice labeling. The source describes a proposed connection with aperiodic tilings and Turing-machine halting, but does not establish the conjecture.