There are two reasons that extrapolation is not a fix for this problem. The first is that the particle system does not CONSISTANTLY lag the object. Every once and a while it will be in the correct spot for a frame and then go back to lagging the object. The second reason is that I do not want to put a Band-Aid on the problem, but understand its root cause and implement a stable solution. At this point, I do not even understand why the particles are being drawn a frame behind.
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