By O’Neill’s definition (§2.5.3 in the report) it’s definitely not equidistributed in higher dimensions (does not eventually go through every possible k-tuple for large but still reasonable k) simply because its state is too small for that. Yet this seems completely irrelevant, because you’d need utterly impossible amounts of compute to actually reject the hypothesis that a black-box bitstream generator (that is actually ChaCha20) has this property. (Or I assume you would, as such a test would be an immediate high-profile cryptography paper.)
replyContrary to GP’s statement, I can’t find any claims of an actual test anywhere in the PCG materials, just “k-dimensional equdistribution: no” which I’m guessing means what I’ve just said. This is, at worst, correct but a bit terse and very slightly misleading on O’Neill’s part; how GP could derive any practical consequences from it, however, I haven’t been able to understand.
As you note, a 256-bit CSPRNG is trivially not equidistributed for a tuple of k n-bit integers when k*n > 256. For a block cipher I think it trivially is equidistributed in some cases, like AES-CTR when k*n is an integer submultiple of 256 (since the counter enumerates all the states and AES is a bijection). Maybe more cases could be proven if someone cared, but I don't think anyone does.
replyComputational feasibility is what matters. That's roughly what I meant by "measurable", though it's better to say it explicitly as you did. I'm also unaware of any computationally feasible way to distinguish a CSPRNG seeded once with true randomness from a stream of all true randomness, and I think that if one existed then the PRNG would no longer be considered CS.