Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 238-12. A strict four-row permanent inequality and permutation moments
Manuscript map · lines 7175–7184
OpenAI@2026-10-07#rem:oai-p-238-12
Authors: OpenAI. Family 238.
Title: A strict four-row permanent inequality and permutation moments.
Abstract: We prove a permanent inequality with exponent strictly below two for laws on S4 sufficiently close to uniform and with exactly uniform coordinate marginals. Applied to a four-row recursion, it shows that an absolute number of coordinate sweeps brings the full permutation of the Thorp shuffle on $N=2{}d$ cards to total-variation distance tending to zero from uniform as $N{}to{}infty$. Thus the mixing time has the optimal order $O({}log N)$ in physical shuffles.
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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