Z₃ Topology in the Hexagonal Bipyramid: Three-Phase Source Geometry and the Independent Derivation of Q = 2/3

We show that the hexagonal bipyramid cavity of Dimensional Oscillation Theory supports a Z₃ (1/3-twist) topology beneath the Möbius (Z₂) condition. The Z₃ primary resonance requires 2 transits (120°), compared to 3 (180°) for Möbius. The Möbius condition emerges as the apparent topology for an observer at 60° on the strip. The hexagon factorizes as Z₆ = Z₃ × Z₂, separating force physics from matter/antimatter duality. Two independent source configurations confirm that force phases (60°, 5.95°, 3.30°) are container properties, invariant under source changes. Sum-frequency interference of Z₃ phases breaks three-fold democracy into a 2+1 split, independently deriving ε² = 2 and the Koide ratio Q = 2/3 from interference physics without equipartition. The 4/3 frequency cascade replicates itself through beating — adjacent beats have ratio exactly 4/3 — providing a mechanism for self-similar structure from atomic to cosmic scales. Seven predictions unique to Z₃ include CMB correlations at 120° azimuthal shift and dark modes at sub-Möbius resonances carrying exactly half the Z₃ spectrum's energy. All results verified numerically with code and outputs provided.