When Does Geometry Beat a Token-Entropy Baseline for Predicting Semantic Entropy? A Robustness Audit of Training-Free Hallucination Signals

Training-free geometric features of transformer hidden states (trajectory curvature, eigenscore, effective rank) have been proposed as cheap, probe-free signals of semantic uncertainty for hallucination detection. We audit whether they deliver rather than proposing a detector, and find that a trivial token-entropy baseline matches or beats every one of them, and that which features appear reliable is set by the evaluation split rather than by the geometry. Across Llama-3-8B-Instruct and Mistral-7B on TruthfulQA, BioASQ and SQuAD v2 (six model-by-dataset cells), we score each feature as a direct predictor of meaning-clustered semantic entropy against the model's mean per-token entropy: one scalar from the same forward pass, computed independently of the answer sampling that defines the target, so the comparison is not circular. Token entropy wins on all five seeds in five of six cells, by a partial-correlation margin of +0.116 to +0.191; geometry fails to beat the baseline it was introduced to improve upon. Eigenscore and effective rank are largely sequence-length confounds: length explains about 98-99% and 58-93% of their variance, and their apparent signal vanishes under nonlinear length control. Curvature, the one length-independent feature, is small (partial r about 0.1-0.18) and redundant with the baseline. At the pre-registered held-out endpoint (n=245) the number of model-by-dataset cells in which curvature's confidence interval excludes zero swings from zero to three across five splits, while the full sample (n=817) is fixed at four. Because more than a third of items sit at the target's floor, with all ten generations collapsing into a single meaning cluster, every correlation reported is an attenuated lower bound; this bounds absolute magnitudes but not the ordering between features, which face an identical target. We argue that any training-free geometric uncertainty feature should be required to clear a token-entropy baseline on equal footing and survive a reseeded held-out evaluation, two cheap checks that the features examined here do not pass.