Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 238-04. Conditional information under deterministic coordinate sweeps
Manuscript map · lines 7095–7104
OpenAI@2026-10-07#rem:oai-p-238-04
Authors: OpenAI. Family 238.
Title: Conditional information under deterministic coordinate sweeps.
Abstract: We bound the information remaining after paths of specified cards in the Thorp shuffle on $n=2{}d$ cards have been observed. After a fixed number of deterministic coordinate sweeps, the joint endpoint law of further cards is close to uniform on the available positions, on average over the observed paths, provided a fixed positive fraction of labels lies outside both lists. Combined with a Fourier transfer, these bounds give full-deck mixing after $2048d$ 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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