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…