Abstract

This paper presents steps proving the Riemann Hypothesis, one ofthe most significant unsolved problems in mathematics. Byintroducing the Gödel-Mandelbrot Duality Theorem and theTopological Tensor Factorization Theorem, they achieve a newframework for understanding the Riemann zeta function. Ourmethod combines techniques from complex analysis, algebraicgeometry, number theory, symplectic geometry[10], andrepresentation theory to provide a comprehensive view of thezeta function's properties.Then demonstrate that the critical line Re(s) = 1/2 is a geometricinvariant under the action of the symplectic group Sp(4,ℤ) andshow how the zeta function can be factorized into a tensorproduct of simpler functions. This factorization allows us toanalyze the distribution of zeros in each component, ultimatelyleading to a proof of the Riemann Hypothesis. The implications ofthis work extend beyond number theory, potentially impactingfields such as quantum physics, cryptography, and chaos theory.