A Minimal Classification of Foundational Results_ Existence, Impossibility, and Uniqueness

Foundational results across mathematics, logic, and theoretical science determine the admissible solution space of a constrained problem. This paper establishes a minimal classification of such results at the level of logical outcome. It is shown that any well-formed foundational result resolves to exactly one of three mutually exclusive and collectively exhaustive types: existence, impossibility, or uniqueness up to equivalence. The classification is proven irreducible and closed under refinement. A formal distinction is drawn between proof operations (such as construction and elimination) and result types. Canonical examples are provided across domains. The result yields a domain-independent structural framework for understanding foundational reasoning and clarifies the roles of construction, constraint, and forcing in determining solution spaces.