Fractal Riemann Hypothesis PART C, A Topological Quantum Field Theory Proof of the Fractal Riemann Hypothesis A Unified Framework Based on Non-Abelian Gauge Field
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2026
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| _version_ | 1866901169596530688 |
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| author | ZHOU, changzheng zhou, ziqing |
| author_facet | ZHOU, changzheng zhou, ziqing |
| contents | <p>This study constructs a unified theoretical framework integrating topological<br>quantum field theory (TQFT) with fractal geometry, aiming to prove the Fractal<br>Riemann Hypothesis, which asserts that all non-trivial zeros of the fractal zeta<br>function lie on the critical line Re(s) = DH/2 (where DH is the fractal dimension).<br>By adapting non-Abelian gauge field theory to fractal manifolds and introducing<br>fractal cohomology theory to define topological invariants, this work reveals the<br>profound intrinsic connection between the self-similarity of fractal structures, the<br>topological phase transitions of gauge fields, and the distribution of the zeta func<br>tion zeros. Theoretical analysis shows that the scaling laws of topological invari<br>ants and the global symmetries of non-Abelian gauge fields jointly impose strong<br>constraints on the zero positions, while the suppression mechanism of topological<br>excitations under renormalization group flow further ensures the stability of the<br>zero distribution. Numerically, for the Sierpiński gasket (DH = log2 3), validation<br>is performed using a combination of topological quantum computing simulations,<br>multi-scale entanglement renormalization ansatz (MERA) tensor networks adapted<br>to self-similar structures, and lattice gauge theory simulations. The results show<br>that the peak of the zero density is located near σ = 0.792, in high agreement with<br>the theoretical prediction DH/2, with an error less than 2%. This study not only<br>provides a new proof path for the Fractal Riemann Hypothesis based on physical<br>principles but also lays a theoretical foundation for exploring topological quantum<br>f<br>ield theory in the context of fractal spacetime.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18220446 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Fractal Riemann Hypothesis PART C, A Topological Quantum Field Theory Proof of the Fractal Riemann Hypothesis A Unified Framework Based on Non-Abelian Gauge Field ZHOU, changzheng zhou, ziqing Fractal Riemann Hypothesis; Topological Quantum Field Theory; Non Abelian Gauge Fields; Fractal Zeta Function; Topological Invariants; Tensor Networks; Fractal Cohomology; Instantons; Renormalization Group; Sierpiński Gasket; Multi-scale Entanglement Renormalization Ansatz <p>This study constructs a unified theoretical framework integrating topological<br>quantum field theory (TQFT) with fractal geometry, aiming to prove the Fractal<br>Riemann Hypothesis, which asserts that all non-trivial zeros of the fractal zeta<br>function lie on the critical line Re(s) = DH/2 (where DH is the fractal dimension).<br>By adapting non-Abelian gauge field theory to fractal manifolds and introducing<br>fractal cohomology theory to define topological invariants, this work reveals the<br>profound intrinsic connection between the self-similarity of fractal structures, the<br>topological phase transitions of gauge fields, and the distribution of the zeta func<br>tion zeros. Theoretical analysis shows that the scaling laws of topological invari<br>ants and the global symmetries of non-Abelian gauge fields jointly impose strong<br>constraints on the zero positions, while the suppression mechanism of topological<br>excitations under renormalization group flow further ensures the stability of the<br>zero distribution. Numerically, for the Sierpiński gasket (DH = log2 3), validation<br>is performed using a combination of topological quantum computing simulations,<br>multi-scale entanglement renormalization ansatz (MERA) tensor networks adapted<br>to self-similar structures, and lattice gauge theory simulations. The results show<br>that the peak of the zero density is located near σ = 0.792, in high agreement with<br>the theoretical prediction DH/2, with an error less than 2%. This study not only<br>provides a new proof path for the Fractal Riemann Hypothesis based on physical<br>principles but also lays a theoretical foundation for exploring topological quantum<br>f<br>ield theory in the context of fractal spacetime.</p> |
| title | Fractal Riemann Hypothesis PART C, A Topological Quantum Field Theory Proof of the Fractal Riemann Hypothesis A Unified Framework Based on Non-Abelian Gauge Field |
| topic | Fractal Riemann Hypothesis; Topological Quantum Field Theory; Non Abelian Gauge Fields; Fractal Zeta Function; Topological Invariants; Tensor Networks; Fractal Cohomology; Instantons; Renormalization Group; Sierpiński Gasket; Multi-scale Entanglement Renormalization Ansatz |
| url | https://doi.org/10.5281/zenodo.18220446 |