Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 140-03. Localization costs and information growth for exact Gaussian observations
Manuscript map · lines 5115–5124
OpenAI@2026-10-07#rem:oai-p-140-03
Authors: OpenAI. Family 140.
Title: Localization costs and information growth for exact Gaussian observations.
Abstract: For the image of a uniform cube under a spherical coordinate map, we prove that finite messages from t blocks of ${}Theta(d)$ exact Gaussian measurements reveal only $O_A(dt)$ information when each message has at most ${}exp(Ad{}2)$ values, for fixed A. The same bound holds when each message is supplemented with a nested cell that restores the required geometric spread.
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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