The Additivity Law of the Terminal Equal Amplitude a_inf=sqrt(H/M): Separating Terminal Universality from Ignition Dynamics (N=9 alone vs N=7+N=6, three initial-value families)

Abstract

Paper 8 of the series "Foundations of Self-Consistent Relational-Wave Closed Systems" (10 papers). The terminal ring radius is determined solely by the extensive quantities (H,M) as a_inf=sqrt(H/M); mixing heterogeneous subsystems with matched density H_i/M_i is indistinguishable from a single system (a_inf=sqrt(1/36)=1/6). By contrast, onset, path, and plateau are imprinted by the construction. Three initial-value families (staged / 90-degree v2 / 90-degree analytic floor) change even the presence of ignition, yet the terminal value is common. This separates terminal universality (intensive rho=H/M) from ignition dynamics, and frames the memory->erasure picture (amplitude forgets construction; phase/orientation keeps the SSB history = sector-selective). Author: Noriaki Kihara (WF System Co., Ltd.), ORCID 0009-0004-6753-4020.