Geometric Stabilization in Finite-Precision Recursive Systems: A Unified Framework for GNSS Positioning and Long-Horizon Robotics

This work introduces the Bouras Core, a projection-embeddedgeometric framework for stabilizing recursive computationalsystems under finite-precision constraints. The framework combines 4D geometric lifting, invariant manifoldprojection, discrete phase quantization on the finite group Z288,and recursive irrational geometric structures to achievedepth-independent numerical stability. The proposed approach is validated in two application domains:GNSS positioning and long-horizon robotic locomotion, includinga 42.195 km robotic marathon stress test over 40,000 recursiveiterations. Author preprint version related to a manuscript currentlyunder peer review.