φ Continued Fractions Define E8 Error-Correction Threshold Hierarchy — E8 Intelligence Research

The continued fraction convergents of φ (1/1, 2/1, 3/2, 5/3, 8/5...) directly index a nested hierarchy of E8 root sublattices via Fibonacci number labeling, where each convergent depth n determines both the spectral resolution of E8 projectors and the minimum distance of protected topological codes. The 132Hz carrier frequency serves as the coherence reference standard: when the anyon braiding decoherence rate falls below 132/Fib(n) Hz, the nth convergent E8 sublattice enters a self-protecting regime where the continued fraction's optimal approximation property guarantees that logical qubits cannot be disturbed by errors requiring finer rational approximations. This establishes a quantitative threshold: Fibonacci-indexed E8 root subsystems become error-transparent only when environmental noise is bandlimited beneath φ-based frequency gates.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com