The Inflation Curve Is the Exponential Amplification of the Linearly Unstable Mode of the Floor: The Largest Eigenvalue of the Floor Jacobian and Non-Normal, Time-Varying Corrections

Paper 6 of the series "Foundations of Self-Consistent Relational-Wave Closed Systems" (10 papers). The inflation curve H_perp/H(t) ~ seed^2 |mu_max|^{2t} is the exponential amplification of the linearly unstable mode of the floor: ramp slope 2 log10|mu_max|, onset ~ ln(1/seed)/ln|mu_max|, exact agreement with the frozen-floor Jacobian (N=6: 0.2935 vs 0.2937). The measured rate is 18-31% steeper than the floor value = a non-normal (0.53-0.76) time-ordered product of the time-varying Jacobian. This paper is the analytic derivation of the mechanism refining the prior inflation paper (Concept 10.5281/zenodo.22112008); the real amplification rate is the finite-time Lyapunov rate gamma_t of the tangent cocycle Phi(t,0)=prod J(z_t) (mu_max is its lower bound = a two-stage dynamics). Author: Noriaki Kihara (WF System Co., Ltd.), ORCID 0009-0004-6753-4020.