Version 3 adds a full introduction, symmetry interpretation, and concluding analysis, and restructures the manuscript into a complete preprint format. This paper continues the series on the principle of energy’s non-opposition by introducing a constraint-based criterion for when sign-opposed configurations must be identified as a single physical state. Using a real scalar field with Z2 symmetry as a worked example, the paper shows that energy, stress–energy, and all invariant observables factor through a quotient space in which apparent oppositional states collapse into a single equivalence class. Treating sign-related configurations as physically distinct is shown to introduce redundant state-counting. The paper further demonstrates that sign becomes physically meaningful only when symmetry is explicitly broken by coupling, establishing a precise boundary between representational opposition and physical distinction.
Gerald Ted Dahlberg Jr (Wed,) studied this question.