ADAPTIVE GEOMETRIC PROCESSING (AGP-SUGRA): A Unified Framework for Topological Moduli Dynamics and Silicon Carbide Heterostructure Interfaces

We present a unified, continuous geometric-processing framework within N=1 Supergravity (SUGRA) compactified on a rigid T^6/Z_3 Calabi-Yau orbifold. To overcome the static constraints of the Isometry Trap, we introduce continuous, time-dependent complex structure deformation vector fields \epsilon(t) that break the unperturbed discrete SU(3) isometry down to its maximal torus subgroup U(1)^2 while rigorously preserving the underlying topological lattice connectivity and Dirac flux quantization. We detail the linear deformation of the holomorphic 3-form \Omega_3(\epsilon) and the corresponding period vector matrix \Pi(\epsilon) across all 36 homology 3-cycles. To dynamically damp transient scalar potential fluctuations V_dyn(t) during state switching, we incorporate an Informational Friction operator U_FI(\epsilon, \dot{\epsilon}, \tau_s) non-linearly coupled to the blow-up Kähler volume modulus \tau_s^* = 4.20. Numerical integration confirms a rapid 94.7% energy dissipation of the scalar potential within t = 2.88 a.u., smoothly relaxing the deformation norm to ||\epsilon(t)|| = 3.88e-3 without static drift in the bulk volume \tau_b^* = 500.00. Finally, we map this topological deformation space to physical state manipulation within active Silicon Carbide (SiC) heterostructure interfaces, offering a path toward dissipationless, topologically protected semiconductor logic.