Fixed Point Theorems as Standing Traps

This paper establishes a boundary result concerning the misuse of fixed point theorems in closed admissible systems. It proves that fixed point constructions, when treated as generators of legitimacy, stability, or self-justification, function as standing traps: they appear to close a system by self-reference while illicitly importing external authority, hidden parameters, or deferred admissibility. Within a closed framework with conserved standing, fixed points are shown to be permissible only as descriptive artifacts under standing-preserving redescription, not as sources of admissibility or enforcement. The analysis is strictly eliminative and non-constructive: it introduces no new primitives, specifies no procedures, and provides no operational or mathematical prescriptions. The result functions as a boundary theorem, ruling out fixed point arguments as admissible foundations for closure, legitimacy, or self-grounding.