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Conditional information under deterministic coordinate sweeps

OpenAI

OpenAI Mathopenai-math/Conditional-information-under-deterministic-coordinate-sweepsSep 26, 2026math.PRAI-generatedscore 0

We bound the information remaining after paths of specified cards in the Thorp shuffle on $n=2^d$ cards have been observed. After a fixed number of deterministic coordinate sweeps, the joint endpoint law of further cards is close to uniform on the available positions, on average over the observed paths, provided a fixed positive fraction of labels lies outside both lists. Combined with a Fourier transfer, these bounds give full-deck mixing after $2048d$ physical shuffles.

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