Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 238-02. Random coordinate frames and partial permutation laws
Manuscript map · lines 7075–7084
OpenAI@2026-10-07#rem:oai-p-238-02
Authors: OpenAI. Family 238.
Title: Random coordinate frames and partial permutation laws.
Abstract: For the Thorp shuffle on $2{}d$ cards, we prove that the worst-start total-variation distance after $32800d$ physical shuffles tends to zero as $d{}to{}infty$. Combining our fixed-list estimate with the companion Fourier transfer improves this bound to $512d$ shuffles. These results follow from bounds on partially observed permutation laws in random coordinate frames.
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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