Abstract: A computer-implemented system generating a structured compatibility certificate prior to invoking a downstream solver within external systems. The structured compatibility certificate is produced by projecting a representation-solver compatibility functional into three mutually exclusive components-relevance, superfluous, and noise-constrained by a normalization invariant. A quality metric derived from semantic decomposition and a compatibility score quantifying geometric alignment between the representation and the downstream solver in a shared latent space converge through conjunction to produce typed execution control that neither signal alone provides.