Spectral Margin Geometry

Spectral Margin Geometry defines the stability margin m=1−ρ(A)m = 1 - \rho(A)m=1−ρ(A) as the central quantitative invariant governing all near-critical behavior in amplified operator systems. The paper shows how margin determines sensitivity to curvature, drift pressure, mixed-gate interactions, observer coupling, and direction-memory violations. Thin margins produce hypersensitivity in basin-restricted spectra, making systems vulnerable to amplification and collapse under even admissible perturbations. The paper provides a full geometric analysis of how margin propagates through reductions, renormalization, and basin restriction, establishing the spectral margin as the universal measure of stability within the Einsteinian Stack.