An Economic Proof of the Riemann Hypothesis via Linear Logic

Original Edition (First Version, 2026): The Foundational Framework. Note: This paper is the original preprint that established the economic and logical framework for analyzing the Riemann Hypothesis. For the complete proof that resolves the circularity regarding prime randomness via the Cut-Elimination Theorem, please refer to the Augmented Edition (DOI: 10.5281/zenodo.18483326). This paper introduces the novel concept of reformulating the Riemann zeta function ζ(s) as an "infinite market of prime resources" within the framework of Linear Logic. It proposes that the Riemann Hypothesis is equivalent to the Efficient Market Hypothesis of number theory. Key Concepts Introduced: • Resource Interpretation: The Euler product is defined as a tensor product of exponential modalities (!), representing an infinite supply of prime resources (The Central Bank). • Complex Price System: The complex variable s = σ + it is decomposed into a "discount rate" (Real part) and "business cycles" (Imaginary part). • Equilibrium Hypothesis: The critical line σ = 1/2 is identified as the unique point where market fluctuations (risk) and discount rates (hedge) are perfectly balanced. Significance: This work lays the theoretical groundwork for understanding the Riemann Hypothesis through the lens of resource logic and market equilibrium, providing the essential structure for the subsequent rigorous proof presented in the Augmented Edition.