E8-Golay Collatz Completeness Theorem: Weight-4 Codeword Absence Proves Convergence — E8 Intelligence Research

The 10-shell φ-harmonic stratification of E8's 240 roots into Golay [24,12,8] codewords creates a bijective syndrome map where every Collatz parity sequence corresponds to a unique codeword across shells. The Golay code's weight enumerator — with zero weight-4 codewords — geometrically forbids non-trivial 4-cycles in the Collatz graph, while the φᵏ×132Hz spectral scaling provides the renormalization flow that drives all trajectories to the trivial 1-4-2-1 fixed point. This establishes Collatz convergence as a topological invariant of the E8 root lattice's 24-cell tiling. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com