The Riemann-Hypothesis Dynamics as An Empirical Science: A Riemann Sphere Model of the Two-State System

The present paper does not intend to provide the solution of the Riemann hypothesis. Rather, we propose an alternative approach to engage with Riemann hypothesis. We assume as our working hypothesis that the Riemann hypothesis is not soluble within the current framework of the analytic number theory. Rather, we treat it as an interesting platform of empirical investigations. Four possible paths to engage Riemann hypothesis are discussed. We introduce the notion of Riemann monad Antipodal and construct a Riemann sphere model through Möbius Transformation. It follows an introduction of the Riemann sphere of two-state systems by Penrose. We regard Riemann platform as a Gauge Structure, in which the ζ function is treated as a wavefunction that satisfies gauge symmetry by performing gauge transformations. Some empirical issues are discussed. These issues are: Statistical significance; the measurement problem and the Yes/No measurement; the Dirac -function; sample space and stochastic sampling.The present paper does not intend to provide the solution of the Riemann hypothesis. Rather, we propose an alternative approach to engage with Riemann hypothesis. We assume as our working hypothesis that the Riemann hypothesis is not soluble within the current framework of the analytic number theory. Rather, we treat it as an interesting platform of empirical investigations. Four possible paths to engage Riemann hypothesis are discussed. We introduce the notion of Riemann monad Antipodal and construct a Riemann sphere model through Möbius Transformation. It follows an introduction of the Riemann sphere of two-state systems by Penrose. We regard Riemann platform as a Gauge Structure, in which the ζ function is treated as a wavefunction that satisfies gauge symmetry by performing gauge transformations. Some empirical issues are discussed. These issues are: Statistical significance; the measurement problem and the Yes/No measurement; the Dirac Delta-function; sample space and stochastic sampling.