Approach Geometry and Deterministic Basin Dynamics Near the Half-Collinear Boundary

A gradient-flow dynamical systems study of configuration organization near the half-collinear boundary in Yang-Mills scattering amplitudes, extending Dunn (2026a) from n=4 to n=4-18. Using a tanh-regularized potential as a structurally grounded ansatz - with physically correct cumulative spinor summation implementing lambda~1..m = sum lambda~_i from Guevara et al. (arXiv:2602.12176) - we identify flat regions surrounding amplitude zero surfaces as the central dynamical feature. Flat regions arise when the cascade of cumulative variables leaves a factor unabsorbed; this is proved constructively by adding one uncoupled factor to a fully-cascaded system and observing the flat region appear. Binary commitment to globally-coherent sign configurations is universal at moderate perturbation across all tested n. Flat regions intensify with n, approaching complete immobility by n=18. We propose the term quarter-collinear regime for this dynamical phase. Classical and phenomenological potential, physically grounded structure - no modification to Yang-Mills theory proposed.