The Spatio-Temporal Structure of the Effective Qubit Hamiltonian: Integrating Thermal Lag (delta_k) as the Infrared Driver

While Quantum Electrodynamics (QED) fully describes the microscopic interaction of superconducting qubits, it lacks the explicit time dependence for macroscopic, non-Markovian environmental modulations. This work updates the HS-angle framework, positioning the Spatio-Temporal Hamiltonians H-effective-k(t) as the necessary infrared (IR) drivers. We formally integrate the Thermal Lag (delta-k) parameter, which quantifies the spatially non-uniform thermal inertia across the quantum chip. The resulting Hamiltonian (Equation 3) ensures the stability of SU(2) symmetry while accurately modeling the observed diurnal frequency drift and the spatial stress gradients. This framework extends the standard QED description to explicitly include geophysical boundary conditions, enabling deterministic correction protocols for fault-tolerant operation.