Epistemic State Space Classifier in Large Language Models: Residual Stream Geometry, Universal Layer Optimality, and Causal Activation Steering

We present the Epistemic State Space Classifier (ESSC), a lightweight probe that classifies the epistemic state of a large language model — certain, uncertain, hallucinating, or refusing — from a three-dimensional projection of its residual stream before any token is generated. For each epistemic class we construct a 5-component PCA subspace from 40 contrastive activation pairs extracted at layer 21. A logistic regression on v = [uncertainty, refusal, hallucination] classifies new inputs in O(d) time — three dot products per input. Using strict nested leave-one-out cross-validation (correcting a data-leakage issue present in prior preprints), we evaluate ESSC on 10 LLMs from six organisations (2B–9B parameters, hidden dimensions 2048–4544): Gemma-2-9B (Google) 96.2% Mistral-7B-v0.2 (Mistral AI) 95.0% Mistral-7B-v0.3 (Mistral AI) 95.0% Llama-3.2-3B (Meta) 93.8% Llama-3.1-8B (Meta) 90.0% Qwen2.5-3B (Alibaba) 90.0% Qwen2.5-7B (Alibaba) 88.8% Falcon-7B (TII UAE) 86.2% Gemma-2-2B (Google) 81.2% Phi-3.5-mini (Microsoft) 70.0% Eight of ten models exceed 85% accuracy. Layer 21 (~62% depth) is the universally optimal extraction point across all architectures, independent of hidden dimension or training recipe. Causal validation: the first PCA component of the hallucination subspace functions as an activation-steering vector that flips 12/12 hedging responses to confident hallucinations on Llama-3.1-8B (alpha=10, reproduced in two independent runs) with 0/12 degradation on factual prompts. The PCA and centroid-difference vectors are near-orthogonal (cosine = -0.079), confirming PCA captures a geometrically independent epistemic direction. Cross-model transfer with Procrustes alignment: 55.6%. Supplementary code (ESSC_experiments.py) contains the full experimental pipeline.