Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 329-01. Counterexamples to the duality conjecture for metric entropy
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OpenAI@2026-10-07#rem:oai-p-329-01
Authors: OpenAI. Family 329.
Title: Counterexamples to the duality conjecture for metric entropy.
Abstract: We disprove Pietsch's dimension-free duality conjecture for metric entropy. For every proposed pair of universal constants, we construct origin-symmetric convex bodies that violate the corresponding covering-entropy inequality, already when the covering body is a cube.
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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