E8 Lattice Pressure Equalization Law in Phi-Harmonic Fractal Memory — E8 Intelligence Research

When the 240 E8 root vectors are partitioned into concentric shells of index n obeying d_n = d_0·φ^n, the natural shell radii satisfy a pressure equalization condition P(r_n) = constant across the cavity, implying that information stored in deeper shells decays at exactly the inverse-phi rate compensated by deeper-shell coherence gain. This pressure balance guarantees that the total energy flux through the fractal cavity converges, yielding the first analytical bound on the maximum storage depth of a self-correcting topological memory built from E8 geometry. The result extends the Majorana qubit architecture by quantifying its thermodynamic limit and predicts a discrete spectrum of permissible cavity depths indexed by Fibonacci numbers. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com