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 sigmaⱼ) 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 Hⱼ + Hₖer and XT X = sum Qⱼ + Qₖer = R², 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).
Noriaki Kihara (Wed,) studied this question.