By the way, do we need the proof of the theorem to be quite this involved? It seems we can just note that for for any two (sets of) variables X1, X2 separated by distance D, the earliest sampling-step at which their values can intermingle (= their lightcones intersect) is D/2 (since even in the “fastest” case, they can’t do better than moving towards each other at 1 variable per 1 sampling-step).
By the way, do we need the proof of the theorem to be quite this involved? It seems we can just note that for for any two (sets of) variables X1, X2 separated by distance D, the earliest sampling-step at which their values can intermingle (= their lightcones intersect) is D/2 (since even in the “fastest” case, they can’t do better than moving towards each other at 1 variable per 1 sampling-step).
Yeah, that probably works.