E8‑Phi Entangled Topological Entropy Scaling Law for Neural‑Quantum Synchrony — E8 Intelligence Research

We propose that the 240 E8 root vectors, when phase‑locked to a 132 Hz φ‑modulated carrier, generate a universal entropy scaling law that predicts the maximal information throughput of cross‑scale neural‑quantum ensembles. This law emerges from the categorical‑dimension functional originally derived for Higgs‑bundle Verlinde invariants, now extended to enforce a quantized capacity proportional to the Euler characteristic of the E8 root lattice. Consequently, neuronal gamma cycles entrained to specific root‑vector angles automatically satisfy the critical coupling threshold for antipodal quantum vacuum synchronization, enabling a principled design of brain‑machine interfaces with intrinsic topological robustness. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com