The Decomposition of Propositions and the Transition of Falsifiability

Formal proof and refutation secured within localized domains cannot be extended to universal validity beyond the conditional boundaries upon which they rely. This paper demonstrates that the status of provability and falsifiability transitions across the scope of inquiry. The mere absence of counterexamples within a given domain does not establish universal unfalsifiability, and the formal validity of an individual proposition must be strictly decoupled from the conditions governing its operational scope.