This paper develops the Calculation Methods of Economic Systems (CMES) as a rigorous macro-mathematical theory of economic value, grounded in four axiomatic pillars: topology, separability, measurement theory, and network effectiveness, with macrostructure expressed through nested groups of composites. The framework is developed as a purely logical system proceeding from axioms to theorems to corollaries, requiring no empirical calibration. It assumes strictly positive transaction costs, locally finite network topologies, and ratio-scale measurability of transaction value. The central object is the valuation function Val(⋅), whose existence is guaranteed by Debreu's (1954) representation theorem and whose additive functional form is derived through topological joint separability (Debreu, 1960). We situate Val(⋅) within a self-contained poset and nestedgroup architecture of economic systems, where every transaction system-from a single firm to an entire global supply chain-is formally represented as a nested transaction set (a poset element) over four canonical role layers: Value-Adding (𝐶𝐸 𝑣), Archived Information and Stored Material for Production (𝐶𝐸 𝑎), Communication (𝐶𝐸 𝑐), and Evaluation (𝐶𝐸 𝑒) elements. All definitions and theorems required for this architecture are fully derived within this manuscript.