Open Research Index

Low-dimensional exact counterexamples to the Recht–Ré inequality

JD Jones

Palomar Registrypalomar/PALOMAR-2026-10-17-000006Oct 17, 2026math.OCscore 0

Five real symmetric PSD 3×3 integer matrices and five complex Hermitian PSD 2×2 Gaussian-integer matrices each have sum 100I and exact norm-of-averaged-product ratio 10329/10000 at n=k=5. The Lean statements use Mathlib positive semidefiniteness over the real and complex fields and the Euclidean operator norm. The rational formalization of De Sa's dimension-five norm-19/16 example is included as a supporting benchmark. The real symmetric dimension-two case is not resolved.

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