Emergent Exchange Coupling and the Universality Hypothesis of the Coherence Ratio in Superconducting Qubits (Paper XIV-D)

We derive the effective exchange coupling J₁₂ between two superconducting qubits mediated by a tunable coupler using a controlled Schrieffer-Wolff transformation in the dispersive regime. This derivation establishes the microscopic origin of the coherent gain parameter J appearing in the Radial Coherential Dynamics (RCD) master equation. We demonstrate that the universality hypothesis α ≡ Γ/J ~ 10⁻⁴ becomes consistent and experimentally falsifiable when explicitly restricted to high-coherence hardware operating with T₂ₛwap ≥ 200 μs and tunable exchange couplings J₁₂ ~ 10-40 MHz. Cross-platform analysis of recent experimental data (IBM Heron/Nighthawk, Google Willow, Rigetti Ankaa-3, IQM) reveals that state-of-the-art devices are entering the regime where the universality test becomes meaningful. The corrected prediction—Γₛwap ~ 1-5 kHz—is consistent with IBM Nighthawk's reported T₁ ~ 350 μs. This paper closes the logical gap between microscopic Hamiltonians and the effective coherence dynamics postulated in RCD, while establishing concrete falsification criteria. Part of the Radial Coherential Dynamics (RCD) Paper Series.