On the Global-Realist Definition of Energy: From the Spacetime-Vacuum Axiom to a Strict Derivation of the Energy Concept

Within the global-realism program, energy should not remain a primitive word inherited from prior formalisms; it must be redefined from the ontology of the theory itself. Building on the spacetime-vacuum ontology of the first manuscript of the series and the Hopf-soliton particle model of the second manuscript, the present paper gives an axiomatic and derivational account of energy inside the same framework. We define the total energy of a spacetime region as the total spacetime-distortion functional of that region relative to the absolutely flat vacuum reference state. Under this definition, rest energy is the minimal locked topological distortion required to sustain an isolated Hopf soliton in a fixed topological sector; kinetic energy is the excess of the total energy of a uniformly moving isolated soliton over its rest energy, and its nonrelativistic form is derived correctly from Lorentz symmetry and the energy–momentum relation; potential energy is the nonlinear distortion difference between a multi-soliton configuration and the sum of its infinitely separated constituents; and radiative energy is the freely propagating dynamical distortion released when topological locking is removed. We further show that the same definition carries a necessary consequence: matter itself is only a protected excitation of the substrate and therefore inherits, in finite or asymptotically rare channels, a universal tendency toward decay and return to vacuum. Metastable higher internal branches decay within a fixed topological sector, particle–antiparticle annihilation removes topological charge by cancellation, and even extremely long-lived composite structures may eventually yield under fluctuation-assisted topological unlocking. We also preserve, for conceptual completeness, two tempting but incorrect internal derivation routes for kinetic energy and explain precisely why they fail: a rigid-translation ansatz and a naive perturbative Lorentz-contraction expansion both attempt to infer kinetic energy solely from partial internal energy bookkeeping, whereas the correct result is fixed by the global conserved four-momentum of the entire configuration. Finally, we argue that apparent cosmological non-conservation of energy and the long-term disappearance of material structure are both artifacts of subsystem bookkeeping unless one works on the global scale that includes the mother background, where total energy remains strictly conserved as total spacetime distortion while local excitations progressively relax toward the flat vacuum state.