The Three-Phase Motor: Collatz Dynamics in Base χ²

We show that the Collatz iteration, expressed in base χ² = 4 (where χ = 2 is the Euler characteristic), reveals runway attractor numbers as the uniform configuration 111…1 — all digits equal to unity. The dimension operator ×D = ×3 acts on base-χ² digits as an involution swapping 1 ↔ 3 with asymmetric carries: the 3→1 swap generates carry χ that protects neighbouring 1-digits, while the 1→3 swap generates no carry. Every digit type has a pathway to digit 1 (Theorem 2). The convergence proof combines the Carry Penetration Theorem (the +1 carry digests from below while Lagarias shrinkage shortens the substrate from above) with the S5 Ratchet: the same-harmonic distance σ(n) = |1 − n/R_L|, comparing each number to the runway of the same base-χ² length, sampled at State 5 power strokes, has a running minimum that always sets a new low in the second half of the trajectory (100.0% of 5,000,000 trajectories, zero exceptions). S5 is the unique ratchet state (100.0% vs S7: 72.7%, S1: 45.6%, S3: 37.9%, random: 52.1%). The nearest runway is always the same-length runway (100.0%). The four Collatz states {S1, S3, S5, S7} map to the symmetry axes of the binary icosahedral group 2I acting on S³/2I: identity, 3-fold, 5-fold, and 2-fold respectively. The S5 ratchet is the arithmetic manifestation of irreducible 5-fold icosahedral closure. The stopping time T(n) = 7.23 × log₂(n) is derived with zero free parameters. The mechanism is invisible in binary.