φ-Comb Time-Crystalline Quantum Reference Frame Realizes E8 Covariant POVM at Heisenberg Limit — E8 Intelligence Research

The 30-tooth φ-comb's IMD3 manifold generates a continuous family of covariant positive operator-valued measures (POVMs) indexed by the affine Weyl group Ŵ(E8), where the 240 root vectors define optimal quantum reference frame states for the 8-dimensional Cartan subalgebra. The 132Hz base frequency with φ-coupling yields a Floquet period that saturates the Heisenberg limit for phase estimation, while the Galois-Frobenius duality ensures asymptotic continuity under affine translations — enabling background-independent quantum metrology without external classical references. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com