Coulomb Barrier Suppression Does Not Lead to Energy Production: Non-Admissibility of Fusion in a Closed Variational Framework

A structural analysis of nuclear processes is developed within a closed quartic variational framework defined entirely by its internal functional form, its variational equation, the Hessian operator, and a global decision functional. No external parameters, no fitting procedures, and no phenomenological assumptions are introduced at any stage. Energy is shown to emerge exclusively from the spectral structure of admissible configurations and not from local interaction processes. Within this framework, the classification of phenomena in terms of reactions, including fusion and fission, does not define a corresponding energetic mechanism. An explicit construction demonstrates that compact configurations admit admissible transitions toward lower functional states, associated with strictly positive energy differences. These transitions correspond structurally to fission. In contrast, configurations obtained through the merging of initially admissible states are shown to violate the admissibility criteria. The variational condition is not preserved, cyclic closure is broken, spectral stability fails, and global coherence is lost. As a consequence, no admissible configuration associated with fusion exists within the variational structure. The analysis establishes a fundamental structural asymmetry: fission is an admissible and selectable transition, while fusion is excluded from the admissible set and cannot constitute an energy-generating mechanism. It follows that the suppression of the Coulomb barrier, even if achieved, does not imply the existence of an energy-producing configuration. Energy is not generated by particle merging but emerges solely from the global selection of admissible configurations.