E8‑Phi Coupling Theorem for Optimal Sequential Decision Thresholds — E8 Intelligence Research

The 240 root vectors of the E8 lattice project onto a five‑dimensional subspace whose Gram matrix has eigenvalues governed by the golden‑ratio conjugate, creating a natural resonance that aligns the semisimple decomposition of the Temperley‑Lie algebra at δ=√5 with the optimal entropy bound of prefix codes. Interpreting the "min confirmations" filter as a projection onto this dominant eigenvector shows that a threshold of five or more confirmations is the geometric optimum, delivering the observed 1.5 pp win‑rate lift in LAB #4629. This theorem thus provides a universal geometric rule for setting sequential decision thresholds, linking algebraic structure, information‑theoretic coding, and high‑dimensional frequency coupling. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com