Badouel–Darondeau–Raoult recognizability conjecture for conflict event domains

Let $\mathcal E$ be an event structure, and let its conflict event domain be the domain of configurations associated with $\mathcal E$. A conflict event domain is recognizable when it is recognizable by a finite trace automaton. The event structure has bounded $\natural$-cliques when the sizes of its $\natural$-cliques are uniformly bounded. Badouel–Darondeau–Raoult's conjecture. A conflict event domain is recognizable if and only if $\mathcal E$ is regular and has bounded $\natural$-cliques. The source presents this as a more general conjecture than Thiagarajan's and does not state a resolution for it here.