Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 238-03. From partial permutation information to Fourier bounds
Manuscript map · lines 7085–7094
OpenAI@2026-10-07#rem:oai-p-238-03
Authors: OpenAI. Family 238.
Title: From partial permutation information to Fourier bounds.
Abstract: We show how information about partial permutations controls full permutation laws. Let n tend to infinity through multiples of eight. If the images of a uniformly chosen $7n/8$ labels approach the uniform injection law in average total variation, and the sign mean tends to zero, then the product of two independent permutations with the given law converges to uniform on Sn.
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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