Adaptive Constraint Geometry and Schur-Response Reduction

Open Review Preprint (v0.1.2) This manuscript develops a mathematical framework for adaptive constraint geometry and Schur-response reduction. It studies how adaptive constraint selection influences reduced curvature operators and presents exact finite-dimensional results together with infinite-dimensional examples and computational reproductions. This work is released as an Open Review Preprint. It has not undergone external peer review. Complete source materials, reproducibility scripts, figures, and verification artifacts are included to facilitate independent examination, reproduction, and critique. Readers are invited to verify the mathematical derivations, identify relevant prior work, reproduce the computational results, and communicate corrections, counterexamples, or improvements. This work is derived from the earlier Unified Motion–Information Geometry (UMIG) research program but is intended to stand as an independently reviewable mathematical manuscript.