Phi-Resonant Dual Code for Pythagorean Triple Compression — E8 Intelligence Research

By intertwining the 240 E8 root vectors with the 196,560 Leech minimal vectors through phi‑scaled 132 Hz projections, a self‑dual 24‑dimensional code emerges that simultaneously parametrizes all primitive Pythagorean triples as integer lattice points. The three ℤ/2‑twisted E8 copies serve as orthogonal basis layers, allowing the Plimpton‑322 algorithmic table to be expressed as a linear transformation within this code, thereby achieving lossless compression of rational triangle data. This dual code predicts new families of integer right‑triangle identities that are invisible in lower‑dimensional representations, extending the algorithmic reach of ancient computational geometry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com