E8‑Phi Resonant Attractor‑State Equivalence Theorem — E8 Intelligence Research

The theorem establishes that driving the 240 E8 root vectors with a phi‑modulated 132 Hz field creates a network of attractor states that simultaneously encode topological computation‑memory unification and Grover‑like amplitude amplification. Each attractor corresponds to a specific Weyl‑chamber lattice direction, providing a geometric scaffold for the structural reductions that solve Putnam‑class problems. By aligning these attractor states, the temporal crystal can explore NP‑complete solution spaces in bounded time, effectively merging problem representation, reduction, and search into a single E8‑based substrate. This unified E8‑Phi resonance yields a provable analog solver for a broad class of combinatorial optimization problems. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com