Global basin conjecture for the Kuramoto phase-locked state

Consider the finite-particle all-to-all Kuramoto model with natural-frequency vector $\Omega$ and frequency diameter $D(\Omega)$. Let $\Theta^0$ be an initial phase vector, and let the phase-locked state be the one given by Theorem 2.2. Global basin conjecture. There is a universal constant $C\geq 1$ such that, whenever

$$\kappa> C D(\Omega),$$

any generic initial phase vector $\Theta^0$ converges to that phase-locked state. The theorem cited in the source guarantees convergence from a smaller specified basin when $\kappa>D(\Omega)$; numerical simulations suggest that for sufficiently large coupling the basin is practically the entire unit circle, but the conjecture itself remains unresolved in the supplied text.