The Minimal Structural Condition of Persistent Reality

This paper derives the minimal structural condition required for the existence of persistent reality. Instead of beginning with physical quantities such as matter, spacetime, or energy, the analysis starts from a weaker requirement: the existence of distinguishable states and admissible transformations between them. It is shown that if all logically possible transformations of the state space are admissible, persistent identity becomes impossible. Under unrestricted transformation any state can be mapped into any other state, forcing every identity assignment invariant under transformation to become trivial. Therefore, any system in which non-trivial identity persists under real transformation must restrict its admissible transformations. This result expresses the minimal structural condition underlying the structural architecture developed in the La Profilée theory.