Critical Slowing Down as a Universal Precursor to Refusal in LLMs: Grassmannian Geometry and Phase Transition Signatures Across 10 Model Families

We present two complementary findings about refusal behavior in large language models. First, Grassmannian subspace analysis across 10 models from 7 organizations shows refusal geometry peaks in the last 5-13% of transformer layers for 7/10 models. Second, harmful prompts exhibit a critical slowing down signature — chaotic lag-1 autocorrelation in layer-to-layer transitions — confirmed across 4 model families (Llama 3.1 8B, Mistral 7B, Gemma 2 9B, Falcon 7B), achieving predictive AUC = 0.9956 using only mid-layer activations before the refusal decision is made.