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 ε4/3+ν2. 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.
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BibTeX
@misc{usami2026conditional,
title = {{Conditional stopping guarantees for a folded parametrization of reduced Stokes vectors}},
author = {Hiroyasu Usami and Ayato Tsuboi and Keisuke Hara},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02421},
eprint = {2611.02421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02421},
}
RIS
TY - UNPB
TI - Conditional stopping guarantees for a folded parametrization of reduced Stokes vectors
AU - Hiroyasu Usami
AU - Ayato Tsuboi
AU - Keisuke Hara
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02421
UR - https://arxiv.org/abs/2611.02421
AB - 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 ε^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.
ER -