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Sharp robustness and stability of the four-row permanent inequality

JD Jones

Palomar Registrypalomar/PALOMAR-2026-10-08-000007Oct 8, 2026math.COscore 0

A formalization of sharp balanced-law robustness and stability refinements of the classical four-row permanent inequalities of Carlen-Lieb-Loss and Bristiel-Caputo. It proves the exact total-variation radius 1/24, optimal variance-deficit coefficient (1-24r)/9, complete nonnegative equality cases, sharp endpoint entropy constants, and adaptive tensorization. The explicit interior exponent is sufficient rather than optimal; at radius zero it is weaker than the classical optimal uniform exponent. Lean checks exhaustive support coverage and exact rational Gram identities.

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