Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 238-05. Conditional permutations in a revealed switching environment
Manuscript map · lines 7105–7114
OpenAI@2026-10-07#rem:oai-p-238-05
Authors: OpenAI. Family 238.
Title: Conditional permutations in a revealed switching environment.
Abstract: Fix half the labels in a Thorp shuffle on $2{}d$ positions and reveal their complete trajectories. We prove that, after an explicit absolute number of coordinate sweeps, the conditional permutation of the remaining labels approaches uniform in expected total variation as $d{}to{}infty$, uniformly in the initial layout. The resulting constructions give full-deck mixing in a constant multiple of d 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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