update: And note in your wager, to win two things have to happen:
1) xor breaks if process repeated with small changes and
2) same for modulo.
Even if I am wrong about 1) and I may well try to prove, I could still win the bet on 2) alone. I can't prove 2) is unbreakable beyond proving that each run is as good as a fixed number of random numbers. But 1) I may well have a go at sometime during the next few years (other projects taking priority for now).
More update: your intuition is clearly a disaster. You are saying that a version which passes NO information from one run to the next is only secure if one that passes some information is secure. That's like saying a house can only be secured by locking all the doors if it is also secure when a door is left open.
-- Enough is enough -- setting tobyink to ignore.
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