This preprint establishes a structural boundary on recursive self-improvement, showing that transitions which redefine a system’s admissibility constraints (L4 semantic jumps) cannot be internally stabilized by a closed single-observer system. The result is formulated within the Scope–Invariance Geometry (SIG) framework and relies on prior notions of semantic stabilization and admissibility retyping developed in Semantification. The paper is intended as a foundational boundary result within the SIG research program.