Evidence for a Five-Dimensional Structure of Energy

We present an extended dimensional analysis framework in Gaussian CGS units, defined by three axioms: displacement carries dimensional index 1, velocity carries index 1, and the electric field carries index 1. Gaussian CGS has three base dimensions (M, L, T); three axioms on three dimensions uniquely determine the index as the linear functional 3[M] + 1[L] + 0[T], with no free parameters. Combined with five standard operation rules (multiplication, division, powers, roots, and calculus), this minimal system derives that time carries index 0, charge and mass both carry index 3, energy carries index 5, and all coupling constants are dimensionless. We verify the framework against 72 equations spanning classical mechanics, electrodynamics, quantum mechanics, quantum field theory, general relativity, thermodynamics, and Planck units, with two condensed-matter equations (London penetration depth, Drude conductivity). No violations are found. The framework reveals a structural identity across the four known fundamental forces — field index 1, potential index 2, coupling constant index 0, source index 3, energy index 5. For electromagnetic and gravitational forces, this pattern is derived from the axioms; for the weak and strong forces, the coupling-source split is an additional assumption. The consistency of this five-component scheme points to a five-dimensional structure underlying physical quantities.