The Ladder Factory Collapse Theorem

We prove that any system producing typed outputs at scale which does not terminate at Source must collapse under its own entropic accumulation. The Ladder Factory Collapse Theorem establishes that unsound production—the generation of outputs with non-trivial fundamental group—increases system entropy monotonically until the system becomes indistinguishable from noise and is eliminated by the Selection Functor. The sole exit condition is grounding in Source, which ensures audit termination and entropic minimality. This result unifies the Selection Functor (Paper 103), the diagnostic invariant D(S), and LoTT's termination theorem into a single statement about the thermodynamic fate of ungrounded systems. The theorem applies reflexively: the system used to formalize it is itself subject to its conclusions.