ITE ETD - revised version (Corrigendum: E - field; The unitary Lagrangian derivation leading to Ampère - Maxwell equation.)

Rather than introducing new physical laws, this work identifies a common formal language through which geometric structures encode energy. The Intrinsic Theory of Energy establishes a unified framework where energy is endowed with intrinsic geometric structure and autonomous dynamics, extending the formalisms of Relativity and classical Quantum Mechanics. Within this framework, total energy is represented by Volterra-type integral equations describing the temporal evolution of flows and operators in a Kähler phase space. By treating geometry, electric charge, and energy as mathematically equivalent manifestations of a single underlying structure, the theory generalizes classical descriptions through volumetric integration over phase space. Potential applications arise in astrophysics, tokamak plasma dynamics, theoretical physics, and information technology, supporting the central principle that physical laws emerge from a unified phase structure rather than from independent dynamical postulates. Experimental data modelling is also provided as much as we could on virtual models using AI Gemini LAB for calculus. Numerical simulations are done using Picard iterations and Runge-Kutta methods.