If our universe is indeed sampled from the speed prior S, then we might well be able to discover the algorithm for the apparent noise on top of the seemingly simple physical laws -- compare Example 1.1. It may not be trivial, as trivial pseudorandom generators (PRGs) may not be quite sufficient for evolution of observers such as ourselves, given the other laws of physics. But it should be much less time-consuming than, say, an algorithm computing the z of Theorem 3.3 which are effectively indistinguishable from true, incompressible noise.
Based on prior S, we predict: anything that appears random or noisy in our own particular world is due to hitherto unknown regularities that relate seemingly disconnected events to each other via some simple algorithm that is not only short (the short algorithms are favored by all describable measures above) but also fast. This immediately leads to more specific predictions.