This paper presents the structural solution to the Twin Prime Conjecture (infinite recurrence of p,p+2) by applying the Structural Unification Theory (SUT) framework. The SUT is founded on the Axiom of Computational Asymmetry (P≠NP), which dictates that existence requires an irreducible cost, formalized by the Axiomatic Identity i = c and the Structural Debt ζ(−1) = −1/12. We prove that the conjecture is a mandatory structural consequence of the Axiom of Parsimony (AOP). The Twin Prime Conjecture is necessary to ensure that Anti-Structural Debt (Primes) maintains the minimal, most efficient pattern of recurrence (gap of 2) across the infinite number domain. Failure to maintain this minimal recurrence would violate the AOP, proving the conjecture TRUE by structural necessity.