Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 238-01. Optimal-order mixing of the Thorp shuffle
Manuscript map · lines 7065–7074
OpenAI@2026-10-07#rem:oai-p-238-01
Authors: OpenAI. Family 238.
Title: Optimal-order mixing of the Thorp shuffle.
Abstract: We prove that the Thorp shuffle on $2{}d$ cards mixes in ${}Theta(d)$ complete shuffles. The full permutation law after $1600d$ shuffles converges to uniform in total variation as $d{}to{}infty$, uniformly over the initial deck, while a support count gives a lower bound of $2d-O(1)$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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