Epistemic Uncertainty Has a Geometric Address: Pre-Generation Subspace Signatures Across 10 Large Language Models

We demonstrate that epistemic uncertainty — a model's internal state of "not knowing" — has a measurable geometric address in the residual stream of large language models, detectable before any output token is generated. Using PCA-based subspace analysis across 10 models from 7 independent organizations, we show that projection scores onto an uncertainty subspace significantly discriminate epistemically uncertain from factually certain prompts (all p < 0.05, most p < 0.001). Two control conditions rule out lexical and topic confounds. **Key Findings** - 10/10 models replicated across 7 organizations (Meta, Google, Mistral AI, Alibaba, TII UAE, Allen AI, Microsoft) - Signal is present **BEFORE** generation — extracted at last prompt token - Two depth clusters correlated with training recipe: - Standard RLHF models: peak at ~62% layer depth - Non-standard training (Gemma-2-2B, Qwen2.5-3B): peak at ~86% depth - Same two exception models previously identified in refusal geometry study (Alieksieienko 2025), suggesting training recipe determines localization of epistemic processing - Three epistemic subspaces (refusal, hallucination, uncertainty) form structured geometry significantly below random Grassmann baseline This work extends the DSAOP framework (Alieksieienko, 2025) and suggests transformers maintain a low-dimensional epistemic state space that can be measured and potentially controlled. Replication code included. All experiments run on Google Colab A100/L4 GPU using Llama 3.1 8B Instruct (4-bit NF4) and 9 additional models. Research conducted in collaboration with AI assistant (Anthropic Claude).