The Mechanics of Undefined: A Layered Energy and Asymptotic Model

This paper challenges the conventional mathematical dogma that views division by zero and asymptotic boundaries as absolute system failures or "undefined" points. By introducing a novel layered energy and transformation model, we demonstrate that algebraic singularities function as geometric gates connecting discrete resolution layers. Through this framework, quantum discretization (such as Planckian quanta) and cosmological phenomena like local Big Bang events emerge as observational artifacts of cross-layer dimensional rotation and asymptotic energy tunneling.