Resolution of Non-Linear Engineering Dynamics via Seonggil Tensor Calculus (STCT) and Advanced Rough Calculus

This paper presents a rigorous mathematical framework utilizing Seonggil Tensor Calculus (STCT) and Advanced Rough Calculus (ARC) to resolve non-linear dynamic instabilities inherent in grand engineering challenges, such as 3D Navier Stokes turbulence and highly coupled chaotic systems. By employing Rough Operator Algebra, we formulate a novel Non-Identity Calculus mapping that bounds non-linear energy cascades. Furthermore, we provide a Python-based numerical proof validating the spectral stability of the proposed Rough Operators via the Gershgorin Circle Theorem, confirming the analytical results and demonstrating the practical applicability of the STCT framework to real-world engineering paradigms.