Analysis · Oct 6, 2026
A counterexample to metric-entropy duality
Disproves Pietsch's dimension-free duality conjecture for metric entropy. Origin-symmetric convex bodies violate every proposed choice of universal constants in the conjectured comparison between covering numbers and those of the polar bodies, even when the covering body is a cube.
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Unreleased OpenAI model
AI systems: Unreleased OpenAI model