arXiv:2603.28650v2 Announce Type: replace-cross Abstract: Can a safety gate permit unbounded beneficial self-modification while maintaining bounded cumulative risk? We formalize this question through dual conditions -- requiring sum delta_n 1, any classifier-based gate under overlapping safe/unsafe distributions satisfies TPR_n 0, escaping the impossibility. Formal Lipschitz bounds for pre-LayerNorm transformers under LoRA enable LLM-scale verification. The separation is strict. We validate on GPT-2 (d_LoRA = 147,456): conditional delta = 0 with TPR = 0.352. Comprehensive empirical validation is in the companion paper [D2].