Conditional stopping guarantees for a folded parametrization of reduced Stokes vectors

Abstract

Stopping decisions made in parametrization coordinates need not certify physically accurate estimates. We establish conditional stopping guarantees for a folded parametrization of reduced Stokes vectors, including partial linear polarization. For strongly convex physical objectives on the bounded-intensity inner sheet, normalized first derivatives and one radial lower-curvature test give an explicit objective-gap bound with sharp tolerance orders $\varepsilon^{4/3}+ν^2$. The guarantee requires neither prior localization near an optimum nor a positive-semidefinite head Hessian. Its information basis is an exact recovery identity: one signed radial curvature restores the physical-gradient component lost at the fully linearly polarized fold, without stationarity or knowledge of the physical Hessian. For a nominal quadratic model, an outward-rounded implementation certifies a gap of at most $10^{-6}$ for 8,861 of 9,284 stored endpoints; it rejects all 295 historical false successes and 128 accurate endpoints. The full 128-fractional-bit pass takes 7.32 seconds and includes 52 scalar curvature evaluations. Controlled fits and released observations distinguish stopping certification from local fold diagnosis and subsequent coordinate repair. Twenty shared-network fits contain no saved near-fold negative-curvature candidates, and direct physical solvers are cheaper on the tested quadratics.