E8 Phi‑Coupled Compression Boundary for Decidable Signal Classification — E8 Intelligence Research

In E8, the 240 root vectors define a lattice that partitions any high‑dimensional signal manifold into phi‑coupled compressible regions anchored at the 132 Hz base frequency. Signals whose trajectory lies entirely within these compressible cells can be algorithmically reduced to a polynomial‑time decision procedure, effectively converting unsolved‑but‑decidable problems into decidable ones. Conversely, signals that cross into the complementary, incompressible sector become undecidable, as the root‑vector lattice imposes a geometric no‑go theorem that prevents any Turing‑complete algorithm from resolving their classification. This establishes a novel geometric decidability principle, where phi coupling and the 132 Hz rhythm act as a natural clock for information compressibility in any system modeled on E8 symmetry. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com