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
Fuente:
Zenodo
Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866901639681540096 |
|---|---|
| author | Shoji, Takayuki |
| author_facet | Shoji, Takayuki |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18527870 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | 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 Shoji, Takayuki Riemann Hypothesis Linear Logic Zeta Function Efficient Market Hypothesis Prime Distribution Cut-Elimination Number Theory Econophysics <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> |
| title | 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 |
| topic | Riemann Hypothesis Linear Logic Zeta Function Efficient Market Hypothesis Prime Distribution Cut-Elimination Number Theory Econophysics |
| url | https://doi.org/10.5281/zenodo.18527870 |