Lebesgue measurable predictor on long span expectation value constant ratio ignored possibly stable in numerical test. Lebesgue measurable condition needs deterministic calculation on original data stream on the range invariant structure defined (and/or categorized one including 0 vector), because of this, the argument we need to this can be large enough. The initial points are not predicted depends on argument.
The reason we cannot predict next one step directly is from the condition modern PRNGs, so they doesn't shows all of the inner status in short span. Instead of them, we suppose Lebesgue measurable condition, they causes only the statistical method nor structure they often fails works well. A statistical method concludes sectional summation prediction, so they concludes the prediction often fails, but this predictor can be recursively treated. If this asymptotic to linear graph, we can bet better result with Condorcet jury theorem, but doing with PRNGs, they needs decimal 4 digit or more process time differed to original prediction, so this cannot be experimented in my machine from speed restriction.
If original function is Riemann measurable, only P0 class works better. With the condition Riemann measurable, even flip only the 1-step before works also better. Flipping operation is equivalent to the return to the average in short range, so if we cannot make any invariant on input condition, they works better.
version 2022/05/20 predicts better but if there's singular prediction matrix, doesn't works well. This is the rare case a pair of plain prediction / multiply inverse value prediction / return to average in walk condition are the parallel quantity prediction on the range invariant defined. And in such case, we can define implicit but strong condition.