Mechanism of Inflation-like Rapid Expansion in Self-Consistent Closed Relational-Wave Systems: Normalization Audit, Rank Generation, Zero-Square-Closure Conservation, Simplex Symmetrization, and Reconstruction of the Axiom System

Sequel to Paper 8 of the dimensional generation series. Paper 8 showed that a closed N-body relational-wave system exhibits, without any external seed, a long latency followed by exponential growth of the component outside the parent plane and a transition to a metastable three-direction structure. This paper re-audits that phenomenon at the level of the code, re-runs N=3-16, and adds a linear-stability study at N=5. (1) The Cayley update of the real antisymmetric generator is a real orthogonal matrix, so both the Hermitian norm and the bilinear zero-square closure are conserved exactly; the expansion is an internal transfer from the parent plane to the transverse sector, bounded kinematically by the total norm. (2) The onset is the linear instability of a self-consistent relative equilibrium: the rotating-frame Jacobian has a dominant real doubly degenerate multiplier 1.090086569 whose prediction 2 ln mu = 0.172514 matches the measured growth rate, and 1/ln mu = 11.593 matches the slope 11.616 of the onset time against minus the log of the measured fixed-point residual (R^2 = 0.99999201); the two-dimensional dominant unstable eigenspace added to the rank-2 parent explains the rank-4 selection. (3) The K/sigma_max normalization of the earlier code is a state-dependent rescaling of the Cayley step; the 6.8% finite-step difference in growth rate per accumulated phase is predicted to 0.13% by the independently measured first-order step-convergence law, so normalization cannot have generated the expansion. (4) Local zero-square closure at every vertex star is equivalent to all simplex vertices lying on the bilinear null cone; together with equipartition the metastable state is an equimodular null complex simplex of Gram rank N-1. (5) The 120-degree separation of the three phase classes at N=4 is a theorem, and the 13 nontrivial two-edge closures and 12 exact covers at N=5 follow combinatorially (3x3+2x2, 3!2!) from the 3+3+2+2 sign-paired class structure; an 8-seed sweep reproduces the class structure while the relative phase between the two distance families varies, indicating a flat direction. (6) The axiom system is reorganized: complex rotating pairs, zero-square closure, and a compact S^1 phase orbit follow from self-consistency, but finite recurrence U^n = I requires a separate rational phase-locking mechanism. Japanese and English full texts with figures and analysis packages.