Universal Post-Tensor Calculus (UPTC): Integrating the Ideal Differential Framework with Non-Commutative Rough Operator Algebra

Classical calculus, grounded in the non-constructive Cauchy-Weierstrass ε-δ continuum limit [1], fails intrinsically when subjected to fractal boundaries, quantum non-commutativity, and high-dimensional complexities. By synthesizing the newly proposed Ideal Differential Framework (IDF) with Advanced Rough Calculus (ARC), Hierarchical Evidence Calculus (HEC), and Post-Tensor Dynamics, we construct the Universal Post-Tensor Calculus (UPTC). This framework replaces abstract limits with algebraic phase transitions mediated by the Seonggil Operator (Ŝ). Furthermore, utilizing Non-Identity Calculus, we demonstrate the topological spectral collapse of differential degrees of freedom, transforming an intractable O(N^D) infinite-task operation into a polynomial O(N^k) exact evaluation, thus bridging continuous topology with constructive discreteness.