Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 096-01. The Gaussian propeller bound in every dimension
Manuscript map · lines 4335–4344
OpenAI@2026-10-07#rem:oai-p-096-01
Authors: OpenAI. Family 096.
Title: The Gaussian propeller bound in every dimension.
Abstract: We prove the Gaussian propeller conjecture: for every finite measurable partition of a Euclidean space, the sum of the squared lengths of its Gaussian first moments is at most $9/(8{}pi)$. For dimension at least two and at least three cells, three planar sectors of angle $2{}pi/3$, extended by an orthogonal Euclidean factor, attain the 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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