When Does Geometry Beat a Token-Entropy Baseline for Hallucination Detection? A Robustness Audit

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. Across two models and three datasets (six model-by-dataset cells), we test each feature as a direct predictor of semantic entropy against a trivial baseline: the model's mean per-token entropy, a single free scalar requiring no hidden states. Geometry fails to beat the baseline it was introduced to improve upon: token entropy matches or beats every geometric feature with a testable length-independent signal, winning on all five seeds in five of six cells, by a partial-correlation margin of +0.116 to +0.191. Two of the most prominent features are largely sequence-length confounds: eigenscore is almost perfectly collinear with length (about 98-99% of variance) and effective rank is 58-93% explained by length and its square, with their apparent uncertainty signal vanishing under nonlinear length control. The one feature with a genuine length-independent signal, representational-trajectory curvature, is small (partial r about 0.1-0.18) and redundant with the free baseline. Most consequentially, the conclusion itself is unstable: the number of features that appear reliable at a held-out endpoint swings from zero to three across random splits, while the full-sample evaluation is fixed at four, so evaluation protocol, not the geometry, often determines the verdict. 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.