Unramified-Geometric Langland Conjectures through Chaotic Number Theory.

In Classical Number Theory, Prime divisibility and Unique factorization rule is suitable for linearly static system which is no longer compatible with the real world phenomena of today. This motivates the development of Unramified-Chaotic Number Theory through Fractional divisibility and Factorization Technique for Unramified-Geometric Langland conjectures in Modern mathematics. These findings may contribute to Unramified-Geometric Langland program, BSD Conjecture, Nonlinear or Chaotic dynamical system modelling, Real-time calibration and adjustment of the system as well as the United Nations SDGs respectively including but not limited to target 3.5 and 8.5 (Substance Abuse Prevention and reducing inequalities as well as unemployment rate). We hope that this work will stimulate further investigation into possible interactions between iteration, number theory and Unramified-Geometric Langland Program. Key words: Finite extension of Rational number system ℚ, Abstract ratio, Power-Algebraic ratio, Exponential ratio, Tetrational ratio, Pentational ratio, Fractional divisibility and Factorization Property and Chaotic Equations.