“ We were able to prove that this generalized system always becomes synchronized, for any number of oscillators and no matter how they started.

A key ingredient is the notion of “absorption”—a shorthand for the idea that if one oscillator kicks another over threshold, they will remain synchronized forever, as if one has absorbed the other.
(…) Once two oscillators fire together, they will never drift apart on their own, because they have identical dynamics; furthermore, they are identically coupled to all the others, so even when they are kicked, they will stay in sync because they are jolted equally.

Thus absorptions act like a ratchet, always bringing the system closer to synchrony.

The heart of the proof is an argument demonstrating that a sequence of absorptions locks the oscillators together in ever-growing clumps, until they finally coalesce into one giant group.”