Barrier-Mediated Transport and the Doubling Mechanism for the Rotational Phase Coefficient

This Theorem establishes the perturbative transport mechanism by which two barrier-crossing legs at scale 1/320 combine to produce a doubled antisymmetric residual at scale 1/160. Under the near-identity crossing model, each leg carrying a shared antisymmetric generator A = E_d with leg-specific symmetric dressing S_n, S_d at scale 1/320, the round-trip operator T = Xd→n·Xn→d expands to: T = I + (1/160)A + (1/320)(S_n + S_d) + O(1/320²) The antisymmetric residual at first order is (T − I)_antisym = (1/160)A. The theorem-side readout of T26–T27 kills the scalar and symmetric components, retaining only the antisymmetric rotational slot, giving μ_transport = 1/160. The doubling 1/320 → 1/160 follows from three structural facts: T7 forbids direct outer-to-outer coupling, T8 gives 1/320 as the exact first mediated suppression scale, and the two-leg crossing structure doubles the contribution at first order. Iterated transport T̃^k = cos(kθ)I + sin(kθ)A with θ ≈ 1/160 approximates smooth phase rotation on the defect plane. After k = 160 cycles, the accumulated phase is of order 1 radian, the discrete-to-continuous bridge consistent with the T36–T37 defect holonomy U_d(θ) = eθE_d. Status: T8 first mediated slot 1/320 solid. T7 middle-mediated structure solid. T̃^k formula exact algebra. Theorem readout kills symmetric terms solid (T26–T27, Lemma 29.1). The near-identity crossing model is an assumption supported by T29–T31 but not proved as literal equality. r = 1 as a primitive crossing slot is a natural identification, not uniquely forced. μ_transport = 1/160 derived under the assumption. Identification μ_transport = μ_theorem is a structural match, projection compatibility deferred to T49. All results inherit T7, T8, T17, T26–T29, T36–T37 conditionality. Dependencies: T7, T8, T17, T26, T29, T36, T37, T47.