Anonymous Equal-Amplitude Composite-Wave Model: Basic Axiom System v7

A pure definition paper for Basic Axiom System v7 of the Anonymous Equal-Amplitude Composite-Wave Model, preserving the concept DOI of v3-v6. Version v7 adds three derived consequences under fixed generators, between Consequence 16.3 and Axiom 17: Consequence 16.4 (plane decomposition and kinematic isomorphism) - a fixed closure-preserving generator decomposes into rotation planes and a null space, the Cayley update rotates each plane by the constant angle 2 arctan(gamma sigma_j) with orientation fixed by K p = sigma q and residual gauge SO(2), the unreadability of Axiom 5 is reproduced at the level of derived plane coordinates, the null space is static, and frequency nondegeneracy is an independent general-position assumption; Consequence 16.5 (double conservation register) - both the energy-like quantity and the squared closure decompose plane-wise and null-space-wise, H = sum H_j + H_ker and X^T X = sum Q_j + Q_ker = R^2, with each term individually conserved; Consequence 16.6 (no-go for spontaneous splitting) - under a fixed generator neither closure nor energy-like quantities move between registers, so spontaneous splitting requires dynamics beyond the fixed generator (sequentially reconstructed generators, nonlinear couplings, or inter-plane exchange), providing the starting boundary for any splitting dynamics. Proofs are given in Paper 4 of the Dimensional Generation Structure series (Concept DOI: 10.5281/zenodo.21468959).