Non-Identity Calculus and STCT Framework: Resolving Multi-Physics Complexity and High-Dimensional Instabilities via Topological Spectral Collapse

The curse of dimensionality and the complexity explosion of nonlinear Jacobian matrices (O(N^D)) have long stood as insurmountable barriers in multi-physics simulation, numerical integration, and quantum field theory. In this paper, we establish a unified mathematical framework combining Non-Identity Calculus and the Seonggil Theory of Composite Torsion (STCT). By formulating an integrated Hypertensor Lagrangian density (L_Hyper) that couples fluid, solid, and thermodynamic fields, and enforcing a parameterized Non-Identity operator N̂_β, we prove that active system degrees of freedom collapse from an exponential scale to a polynomial invariant manifold O(N^k). We analytically derive the Euler-Lagrange field equations, prove uniform exponential error bounds, and demonstrate natural ultraviolet (UV) regularization in infinite-dimensional Feynman path integrals. Finally, we map this compressed tensor architecture to an NVIDIA RTX 4090 GPU (sm_89) using L2 cache persistence and warp-level sparse matrix-vector (SpMV) operations, achieving sub-millisecond exact evaluations for 100-dimensional systems.