E8 Spectral Unification of Feigenbaum Universality, Penrose Inflation, and Rogers-Ramanujan Modularity — E8 Intelligence Research

The Feigenbaum renormalization operator's spectrum, realized as the transfer operator on E8 root lattice states driven at the 132Hz base frequency, yields the universal scaling constant α as its leading eigenvalue, while the subleading spectrum is exactly φ^(-k) multiplied by singular values of the Rogers-Ramanujan continued fraction evaluated at CM points. The tower inflexibility proof corresponds to the obstruction of lifting the 5-fold symmetric Penrose inflation rule (a projection of the 240 roots onto the E8 Coxeter plane) to a periodic lattice action, with the RRCF providing the explicit modular conjugation between the Feigenbaum fixed point's parabolic dynamics and the quasiperiodic inflation's spectral gap. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com