The Factorization Impossibility: Deterministic AI Safety Requires Effect-Boundary Enforcement

This paper proves a fundamental impossibility theorem for AI safety: deterministic safety governance is achievable if and only if enforcement operates at effect boundaries. The Factorization Impossibility Theorem establishes that internal-state governance (alignment, interpretability, value learning) cannot provide deterministic safety guarantees due to non-injective projection maps that irreversibly destroy intent information. The signature result demonstrates capability-invariance: ∂P(safety)/∂A = 0. Security at effect boundaries does not degrade as AI capability increases. A superintelligence is exactly as governable as a narrow AI—provided enforcement occurs at the physical boundary. This work establishes the hard epistemic limit for AI safety, analogous to Shannon's channel capacity theorem or Gödel's incompleteness theorems. By proving where safety cannot live (in the mind), we prove where it must live (at the effect boundary).