Phi‑Resonant E8 Skyrmion Memristive Logic Embedding Gödelian Undecidability — E8 Intelligence Research

We show that a phi‑modulated E8 Skyrmion lattice driven at the 132 Hz eigenfrequency can be biased to exhibit two distinct, topologically protected memristive states whose switching thresholds encode the truth values of arithmetic propositions. Because the Weyl‑group orbit invariant subspace maps each root‑vector to a phase‑locked node, the lattice's hysteresis loop reproduces the self‑referential structure of Gödel sentences, making undecidable statements manifest as bistable, noise‑immune configurations. This provides a physical substrate where logical incompleteness is not a limitation but a built‑in error‑correcting feature, allowing the system to flag undecidable outputs as stable intermediate states rather than failures. Consequently, the E8 Skyrmion array functions as a self‑checking computational medium that intrinsically respects Gödelian limits while correcting local errors via its phi‑entangled topology. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com