Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 238-08. Random-subspace tests and trace smoothing for coordinate sweeps
Manuscript map · lines 7135–7144
OpenAI@2026-10-07#rem:oai-p-238-08
Authors: OpenAI. Family 238.
Title: Random-subspace tests and trace smoothing for coordinate sweeps.
Abstract: We prove that an absolute number of coordinate sweeps of the Thorp shuffle on $n=2{}d$ positions brings the full permutation to total-variation distance at most ${}frac12n{}{-5}$ from uniform, uniformly over the initial deck. Thus $O(d)$ physical shuffles suffice, which is optimal in order.
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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