Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 238-11. Conditional coordinate sweeps and analytic transfer
Manuscript map · lines 7165–7174
OpenAI@2026-10-07#rem:oai-p-238-11
Authors: OpenAI. Family 238.
Title: Conditional coordinate sweeps and analytic transfer.
Abstract: For coordinate sweeps with near-uniform line laws and line sizes among powers of two in a suitable fixed interval, we prove a Schatten-moment bound after conditioning on any feasible collection of prescribed card trajectories. An analytic transfer to binary sweeps then shows that a fixed number of sweeps mixes the Thorp shuffle on $2{}d$ cards in $O(d)$ physical steps, matching the order of the support lower 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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