Fixed Points IV: Curvature, Centroid Motion, and Structural Transitions

Corrected fifth edition. This paper rebuilds curvature coupling and structural transitions on the corrected Fixed Points I-III control framework. It proves perturbative persistence of a separated curved spectral cluster, defines the corresponding Riesz projector and leakage term, distinguishes natural projective-module transport from bare compression and Feshbach reduction, derives intrinsic first-order centroid modulation through a Karcher mean, and gives conditional sign and energy-barrier criteria. Scope boundary. Curvature, overlap magnitude, or positive damping alone does not select attraction, merger, a post-transition basin, the physical q79 endpoints, or a fundamental action.