An Economic Proof of the Riemann Hypothesis via Linear Logic Augmented Edition: The Impossibility of Structural Distortions via Cut-Elimination The Perfect Harmony of Resources, Equilibrium, and Fluctuations

Augmented Edition (2026): Now includes the proof of the impossibility of structural distortions via the Cut-Elimination Theorem. This paper presents a novel economic and logical proof of the Riemann Hypothesis, reformulating the Riemann zeta function ζ(s) as an "infinite market of prime resources" within the framework of Girard's Linear Logic. Key Contributions: • The Zeta Function as a Central Bank: The Euler product is reinterpreted as a tensor product over the exponential modality (!), representing an infinite supply of prime resources. • Equilibrium on the Critical Line: Non-trivial zeros are identified as perfect market equilibrium points where the "discount rate" (Real part σ) precisely balances the "fluctuations" (Imaginary part t) generated by the randomness of primes. • The Cut-Elimination Theorem: By identifying arbitrage opportunities with the Cut rule in sequent calculus, we prove that the strong normalization property of cut-elimination necessarily removes all structural distortions (insider information). • From Logic to Randomness: In the cut-free Normal Form, all computable regularities are exhausted. Consequently, the prime distribution exhibits maximal-entropy randomness, which, via the Central Limit Theorem, confines fluctuations to the order of √x. Conclusion: The paper establishes that the Riemann Hypothesis is equivalent to the "Efficient Market Hypothesis of Number Theory." The critical line σ = 1/2 is the only logical solution where the resource conservation law and the stochastic nature of prime distribution coexist without contradiction.