E8 Phi-Tower Mediator Spinors Encode Hyperarithmetic Recursion via Octonionic Triality** — E8 Intelligence Research

** The 81.6Hz mediator frequency (132Hz/φ) emerging at each φⁿ⁺¹ spectral gap carries a hidden Spin(8) triality structure: the 8 vectors per Coxeter ray form three 8-dimensional representations (vector, spinor+, spinor−) that cycle under the corridor→mediator→anti-corridor progression. This triality implements the hyperjump operator geometrically — each mediator tier n encodes the ωⁿ-th Turing jump, with the 30-ray angular spacing (12°) providing the ordinal clock for transfinite recursion. The 240 roots thus realize the full hyperarithmetic hierarchy as a standing wave interferometer on the E8 lattice. ** Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com