We derive analytically that the optimal feedforward phase for ZZ-coupling correction in superconducting qubits is given by the argument of the first circular moment of the accumulated phase distribution: φ* = arctan (S/C), where C = ⟨cos φ⟩ and S = ⟨sin φ⟩. A negative second derivative proves this is always a maximum. We measure GPS = Pff − Pᵣef on IBM Heron r2 processors (ibmₖingston, ibmₘarrakesh; five qubit pairs) and IQM Garnet (Crystal 20). A robust empirical invariant is observed: π νZZ τ* ≈ const ≈ 0. 873 rad, confirmed across five independent IBM configurations (π νZZ τ* = 0. 873 ± 0. 001 rad). A preliminary τ-scan on IQM Garnet shows a GPS sign reversal consistent with a zero-crossing near φ = 0. 873 rad. The result establishes a robust empirical invariant within superconducting architectures, enabling feedforward calibration without full phase tomography. Related work: - EEDT Protocol: https: //doi. org/10. 5281/zenodo. 19029431- Bell Decay Clock: https: //doi. org/10. 5281/zenodo. 19367565- Software (Quantum-6502): https: //doi. org/10. 5281/zenodo. 19160835
Takeshi Okuda (Wed,) studied this question.