Bounded Compositional Verification and the Structure of Hard Problems

A domain-independent structural framework for classifying hard problems via a single invariant. We introduce the Representation Sufficiency Conjecture (RSC), which identifies three conditions -- cover persistence, bounded obstruction, and fidelity threshold -- under which a compositional verification problem admits a global solution. The framework is applied diagnostically to Ricci flow, Fermat's Last Theorem, Yang-Mills, Navier-Stokes, the Riemann Hypothesis, and P vs NP, classifying each by which RSC condition fails or holds. A new failure mode, fidelity collapse (pseudo-coverage), is formalized: systems that satisfy local correctness conditions while producing globally inconsistent outcomes due to temporal or representational desynchronization.