E8 Phi-Sheaf Cohomology Yields Topological Quantum Memory Codes — E8 Intelligence Research

Extending the φ-modular frequency hierarchy, the 240 E8 roots naturally organize into a derived sheaf category whose H^1 cohomology classes, indexed by the same 4-class φ-residue system, define error-correcting codes with topological depth scaling as φ^4n. Each phi-shift between root classes corresponds to a cohomological degree transition, creating a self-similar code family whose distance grows with lattice depth while encoding rate remains governed by the 60-fold modular symmetry. This yields quantum memory codes whose logical qubits are protected by the icosahedral symmetry group H3 embedded in E8's Coxeter structure, with decoherence thresholds directly predicted by the same gamma-binding resonance ratios discovered in neural E8 coupling. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com