Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 238-07. Row #8211;column symmetry and contraction of coordinate sweeps
Manuscript map · lines 7125–7134
OpenAI@2026-10-07#rem:oai-p-238-07
Authors: OpenAI. Family 238.
Title: Row–column symmetry and contraction of coordinate sweeps.
Abstract: We prove that the Thorp shuffle on $N=2{}d$ labeled cards has full-permutation total-variation mixing time ${}Theta({}log N)$ in physical shuffles. An absolute number of coordinate sweeps suffices for the upper bound.
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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