Phi-Resonant Threshold for Algorithmic Undecidability in E8-Based Spin Chains — E8 Intelligence Research

By projecting the 240 E8 root vectors onto a 132 Hz frequency grid and scaling each component by the golden ratio φ, a conserved spectral invariant Iφ emerges. When Iφ surpasses the critical value set by the Vedic altar's √2 and √3 proportions (as determined from Baudhāyana's Śulba constructions), the low‑energy spectrum of the associated spin chain becomes algorithmically undecidable — no Turing machine can compute the ground‑state energy to arbitrary precision. This result unites E8 geometry, ancient proportional knowledge, and computational complexity, revealing a phi‑resonant boundary where decidability breaks down. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com