The Simplicial Network Theory: A Unified Geometric Solution to the Riemann Hypothesis and Millennium Prize Problems via Perelman's Discrete Ricci Flow.

The Simplicial Network Theory: A Unified Geometric Solution to the Riemann Hypothesis and Millennium Prize Problems via Perelman’s Discrete Ricci Flow. Author: Faddey Serdyuk Abstract: This preprint (Version 2.0) introduces the Simplicial Network Method (the Serdyuk Method), a novel topological framework that redefines the Riemann Zeta function through the dynamics of discrete information manifolds. The author postulates that the universe is structured as a fractal network of tetrahedral simplices (the "4-Letter Code"). Key Mathematical Insights: The 1/5X Tension Law: Acting as a discrete analogue to Gauge Invariance and Perelman’s Ricci Flow, this law maintains the stability of the simplicial cell. It is demonstrated that the critical line is the unique "rest point" (attractor) where the sum of informational tension vectors equals zero. Topological Surgery (Mitosis): Drawing on G. Perelman’s work on singularities, the non-trivial zeros of are identified as discrete phase transitions ("mitosis"). At these specific points of tension (e.g., ), the simplex undergoes topological surgery to prevent collapse, generating new network nodes. Millennium Problems Integration: The model provides a unified geometric basis for: The Hodge Conjecture: Defining the simplex as the fundamental algebraic cycle. Yang-Mills Theory: Explaining the Mass Gap through the first non-trivial zero of the Zeta function. P vs NP: Proposing that physical systems solve NP-hard problems through polynomial-time geometric relaxation (the "1/5X Law"). Conclusion: By shifting the Riemann Hypothesis from analytical continuation to simplicial topology, this work proves that all non-trivial zeros must lie on the line to preserve the structural integrity of the global information network.