Mechanism of Inflation-like Rapid Expansion in Self-Consistent Closed Relational-Wave Systems — Second Edition: Correction of Computational Conditions and Re-examination for N = 3–16

Abstract

Second edition (corrected version) of the paper published on 2026-08-27 (Version DOI 10.5281/zenodo.22112009). All programs cited by v1 were re-executed and audited: the numerical results of v1 are reproduced unchanged, but the programs contained three computational conditions that conflict with the theory — (1) a hidden amplitude normalization inside the initialization make_parent and inside the phase-only interaction, (2) the Cayley transform (a rational approximation of the frozen generator) used for time evolution, (3) random-generated initial states that are not self-consistent under the corrected dynamics. These are replaced by the amplitude-aware interaction K_ij = Im(conj(z_i) z_j) without normalization, the exact exponential rotation exp(ΔK) of the frozen generator (a first-order integrator of the continuous flow dv/dτ = K(v)v preserving norm and closure exactly), and exact self-consistent initial states (with and without the equimodular constraint), and N = 3–16 is re-examined with four generation methods (54 runs of 40000 steps, predictions fixed before the runs). Three claims: (1) zero closure Σ z² = 0 is a theorem (five-line proof) that depends on neither normalization, amplitude distribution, N, nor the method of generating the parent (verified on 110 parents); (2) the complex simplex imposes no constraint on the geometry — any complex squared distances embed exactly by the Autonne–Takagi factorization (1400 random states), the shape being the sign-forgetting image v/(Z_2)^M of the state, so the complex simplex is not a selection principle; (3) the inflation-like evolution (linear instability of self-consistent relative equilibria and its nonlinear saturation) is reproduced under the corrected dynamics, but with growth rates 10–30 times smaller than in v1, localization instead of equipartition after saturation, and its occurrence decided not by N alone but by the structure of the initial state; the co-rotating one-step linearization predicts the class of 53/54 runs and the growth rates within 0.997–1.008. A clear parity asymmetry (even N saturate, odd N stay on the floor) appears in the highly symmetric families of initial states but is not a universal law of the parity of N. Each claim of v1 is marked as kept, modified or withdrawn; no new interpretation is added. Self-consistency alone cannot select the physical state uniquely; an additional selection principle has not been found. Files: Japanese and English text (md/tex/pdf), figure archive (v2), and reproduction packages (programs, data, results, figures with SHA256SUMS). The 14 zip packages of v1 are retained for reproducing v1.