This comprehensive technical report documents the complete development of the Wexp/T Algebraic Calculus framework, a paradigm-shifting mathematical system that replaces classical analysis with exact algebraic computation and constitutes a strictly superior, unified framework compared to my preliminary 2025 works on TVS and algebraic methods. The work includes: FOUNDATIONAL FRAMEWORK: Definition of the dynamic algebraic ring, basis auto-extension algorithm, and matrix representations of differential operators (derivative matrix D, multiplication tensor M). EXACT ODE SOLUTIONS: Algebraic resolution of classical differential equations (Airy, Bessel, exponential-coefficient ODEs) without limits or approximations, demonstrating how "special functions" emerge as algebraic generators. ALGEBRAIC PROBABILITY THEORY: Complete deconstruction of Chernoff bounds and the Central Limit Theorem, showing that probability inequalities are artifacts of insufficient algebraic representation. Includes exact computation of tail probabilities via Laplace matrix transforms. ALGEBRAIC TURBULENCE THEORY: Derivation of the Kolmogorov k^{-5/3} spectrum from first principles using the Hermite-Gauss basis and exact interaction tensor coefficients, together with a proof of finite energy cascade termination (Algebraic Kolmogorov Cutoff Theorem). COMPUTATIONAL IMPLEMENTATIONS: Python algorithms for dynamic basis extension, exact ODE solving, and algebraic turbulence simulation. PRIORITY DOCUMENTATION: Forensic technical comparison establishing November 2025 priority for the Wexp/T framework over subsequent reformulations, explicitly clarifying how this 2026 formulation subsumes and improves all my 2025 TVS-related manuscripts. This document serves as the complete theoretical and computational foundation for the Structured Vacuum Theory (TVS) and represents a fundamental shift from analytic approximation to algebraic exactness in mathematical physics, consolidating and surpassing all earlier 2025 developments in a single coherent framework. This work, including all theoretical developments, text, figures, and associated code, is released under the MIT License. Any use, adaptation, or extension of these results is permitted under the terms of the MIT License, provided that proper attribution is given by citing this report and preserving this copyright and license notice