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| Главный автор: | |
|---|---|
| Формат: | Recurso digital |
| Язык: | английский |
| Опубликовано: |
Zenodo
2026
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| Предметы: | |
| Online-ссылка: | https://doi.org/10.5281/zenodo.18527870 |
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- <p>Augmented Edition (2026): Now includes the proof of the impossibility of structural distortions via the Cut-Elimination Theorem.</p> <p>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.</p> <p>Key Contributions:</p> <p>• 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.</p> <p>• 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.</p> <p>• 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).</p> <p>• 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.</p> <p>Conclusion:</p> <p>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.</p>