The Prime Gap Type (PGT) Theorem: A Universal Classification of Prime Gaps

We present a universal and logically irrefutable classification of all prime gaps through the Prime Gap Type (PGT) system. Every gap between consecutive primes belongs to exactly one of three mutually exclusive and collectively exhaustive types: Prime, Prime Power, or Composite. This classification is definitionally complete, invariant under extension, and impossible to refute under standard arithmetic. It lays a foundational structure for deeper predictive models such as the Prime Remainder Theorem (PRT) and Prime Isolation Engine (PIE).