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

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-27
DOI
https://doi.org/10.5281/zenodo.21617154
Primary Topic
Quasicrystal Structures and Properties
Type
preprint
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preprint

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

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
preprint

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

Andrew Stewart Caldin
preprint en

Abstract

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

Zenodo (CERN European Organization for Nuclear Research)
Decent work and economic growth
Quasicrystal Structures and Properties
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