Hyperbolic event-domain conjecture for Thiagarajan and Badouel–Darondeau–Raoult

Let an event domain be the domain of an event structure, and call it hyperbolic when its underlying graph is hyperbolic. Hyperbolic event-domain conjecture. Conjectures Thiagarajan's and Badouel–Darondeau–Raoult's are true for hyperbolic event domains. The source says this generalizes a theorem for strongly hyperbolic regular event structures and known results for context-free domains, but gives no resolution in general.