This update to the Quantum HS-angle Theoretical Note (V4.5) formally integrates the spatio-temporal dynamics discovered in the latest experimental data (V1.3). The core change is the introduction of the Thermal Lag (delta-k) parameter into the effective Qubit Hamiltonian (H-effective). While previous versions only modeled the time dependence of the diurnal cycle, V4.5 introduces a spatial phase shift delta-k that is unique to each qubit k. This parameter quantifies the specific thermal inertia of the qubit's location on the chip, confirming that environmental noise is not only periodic but also spatially non-uniform. The new Hamiltonian formulation (Equation 3) maintains SU(2) symmetry while providing the necessary framework for highly localized, deterministic correction protocols, moving the field closer to reliable Fault-Tolerant Quantum Computation (FTQC) during periods of high environmental noise.

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.