https://en.wikipedia.org/wiki/Fair_coin#Fair_results_from_a_...
But that only requires you to run the machine with the same coins/dice in the shakers for two consecutive cycles. And to repeatedly do so into you have generated the desired length of 0/1 bit stream.
Bear in mind the machine is fully configurable/programmable. You always choose what goes into the shakers, how many cycles are run, for how long they shake, how vigorously they shake, and what are done with with the 1's and 0's that result.
Implementing Von Neuman's algorithm on the Satoshi9000 is trivial.
Not fully actually:
https://plato.stanford.edu/entries/determinism-causal/#ClaMe...
what is the point in having a source of randomness if you need to XOR with a random source? relatedly, if you have a source of randomness, (1) please share and (2) well, there's no real need to go down this particular rabbit hole at all, well, is there?
independent of all of that, you seem to be anthropomorphizing the XOR function a bit... sure, there are some contexts where "1"s "mean" something and "0"s don't (sparse coding? and yeah, that is some pretty generous contortion, but hey: we're all friends here, right?), but in the case of "randomness"* the whole point (presumably) is that predicting "1"s and predicting "0"s are both exactly the same thing: Sisyphean.
i'm not sure that the word "random" "means" any thing beyond "distribution that we cannot model". which is a fine definition, given that models are how we attack random number generation...
* mind you i challenge the reader to pray tell what "randomness" even really means in anything other than a pseudorandom context (aka used to justify the randomness of various algorithms). isn't it oddly instructive that we use something that would pass as a proxy for "random"ness as the basis for our official definition for the second? (Cesium-133). the "second" is no more real than it is random. random is defined via a threshold of non-randomness, and all that we value as discrete and integral in the world that exists beyond our minds (-- if it does, in fact, even exist (or even "exist")--) is a house built upon sand. well, worse than that: the universe "works" because Avogadro's Number is a hell of a lot closer to infinity than it is to zero, and that's good enough for me. log(N) < 100.
I suggest that any system like this has the output XOR'ed with another random source. If two random sources are XOR'ed together, then both need to be predictable for the output to be predictable.