Constraint Space Computation (CSC): Exact Counting and Existence Verification Without Candidate Enumeration

Classical approaches to counting and existence problems in constrained combinatorial spaces operate by traversal: candidates are generated, filtered, and accumulated. This becomes computationally infeasible as spaces scale, even when constraint structure makes most configurations impossible. This paper presents Constraint Space Computation (CSC), a research framework for determining existence and exact multiplicity of solutions to constrained combinatorial problems by operating at the level of the constraint space itself, without enumerating candidate solutions. Across ten structured validation stages encompassing 212 benchmark tasks in four distinct problem domains, CSC results matched brute-force exact ground truth in every case, with zero failures. The paper describes the research question, evaluation methodology, validated scope conditions, and classes of problems to which CSC does not apply. Core computational mechanisms are proprietary and are not disclosed here.