Rigorous interval-arithmetic certification of numerical inputs

Establish rigorous interval-arithmetic certification for the covariance and singular-value-decomposition inputs used in the correlated-Gaussian fluid-antenna calculations.

Background

The numerical study uses positive Bessel-feature approximations, high-precision recomputation, covariance-entry checks, and residual-variance cushions to control numerical error. These checks do not constitute a fully rigorous interval-arithmetic certification of the covariance matrices and SVD inputs. Establishing such certification would strengthen the formal reliability of the reported rank and outage certificates by enclosing the numerical linear-algebra inputs themselves.

References

These sensitivity checks leave rigorous interval-arithmetic certification of the covariance and SVD inputs open.

— Certified Outage Dimensioning of Fluid Antenna Receivers: Required SNR, Aperture, and Port Count  (2610.13094 - Shen, 9 Oct 2026) in Section V-A, “Protocol, Controls, and Reproducibility”

Dense controls at $W=3$, $N=121$ and 241 remain unresolved.

— Certified Outage Dimensioning of Fluid Antenna Receivers: Required SNR, Aperture, and Port Count  (2610.13094 - Shen, 9 Oct 2026) in Section V-G, “Scattering Sensitivity and Consistency Controls”

Another 5000-block history has a verified confidence-set member outside that region, so direct transfer is unavailable and its additional-member risk remains unresolved.

— Finite-History Outage Certification for Partially Observed Fluid Antenna Receivers  (2610.21252 - Shen, 15 Oct 2026) in Section VI-C, Fixed-Policy Recalibration Controls