Post-Lock Geometry: Double Rotation and the 4-Dimensional Span, and that Plane Switching Is Not an Aggregation Artifact of Long-Window SVD

Paper 7 of the series "Foundations of Self-Consistent Relational-Wave Closed Systems" (10 papers). After the lock, the state is instantaneously rank 2 (a real orthogonal rotation z_t=M_t z_0). Under SSB the floor plane P_0 tilts, and the two principal angles between P_0 and the terminal plane P_term are both nonzero (dim(P_0+P_term)=4). The tilt is 14.2-29.0 degrees over N=6..40. The identity H_perp(t)/H = (1/2)(sin^2 theta_1 + sin^2 theta_2) = (1/4)||Pi_t - Pi_0||_F^2 holds for all t. The SO(4) double rotation as global dynamics is rejected (M_t S != S); what is retained is instantaneous rank 2, the 4D span with two nonzero principal angles, and that plane switching is real (not a long-window SVD aggregation artifact, separated by a short-window SVD test). Author: Noriaki Kihara (WF System Co., Ltd.), ORCID 0009-0004-6753-4020.