L1 Closure Taxonomy What Closure Is and Is Not

This paper provides a precise taxonomy of closure as it applies to foundational inquiry. It distinguishes closure-by-exhaustion from construction, consensus, approximation, or empirical saturation, and formally excludes common misclassifications of closure used in mathematics, physics, and philosophy. The central result is that closure is not a claim about completeness of description, predictive success, or explanatory richness, but a structural condition reached when all admissible alternatives are exhausted. Once closure is achieved, no further admissible extensions, refinements, or reinterpretations exist within the defined scope. The paper also identifies what closure explicitly is not:it is not finality of knowledge, not denial of contingency, not elimination of novelty, and not a global claim about reality. Instead, closure is shown to be scope-bound, binary, and auditable in principle. This work establishes the conceptual ground rules required to interpret subsequent closure and impossibility results correctly, preventing illicit scope expansion, redefinition, or retroactive weakening of claims. It introduces no procedures, constructions, or operational systems. Keywords: closure, exhaustion, admissibility, scope, foundations of science, impossibility results