Let's assume a simple algorithm like the Skein hash function.
Is it possible, given the algorithm, to construct a proof that it does not have a particular distinguisher, something like:
$P(xyz)$ is the probability that $xyz$ is truly random over some alphabet,
Given $\vert y \vert = l$, for some fixed length l, $z = f(x)$ (i.e., $z$ is dependent on $x$).
Not in general, of course, but for a particular such distinguisher.