This paper formalizes Level Ascension, a cognitive-structural operation whereby a phenomenon, conflict, or paradox that resists resolution at level L is shown to be a necessary projection of a generative structure at level L+1. The operation is defined by three necessary conditions — intractability at L, generativity of the L+1 structure, and formal derivability of the L phenomenon from that structure — and one falsifiability condition specifying the primary failure classes under which the operation produces false or incomplete results. The operation was identified as the common structure underlying two independently developed cognitive operations: Impossible-First Reasoning and the Unification Method (归一法). The paper demonstrates the generativity of the resulting execution architecture across four independent domains: formal ontology (Domain of Non-Existence), relational geometry (Dimension Convergence Model), institutional governance (System of Eternity), and physical cosmology (Chameleon Gravity Effects Model), the last including the falsifiable prediction ΔH/H ∼ β²|δ|. Failure conditions, including hard constraints, motivated ascension, incomplete ascension, and iterative regress, are formally specified.