Large language models can hallucinate with the same fluent confidence they bring to correct answers, making reliable hallucination detection essential for trustworthy deployment. Existing detectors based on LLM hidden states often rely on cosine or linear readouts that ignore the anisotropic structure of the representation space. We introduce DTS (Discriminant Truthfulness Scoring), a lightweight, gradient-free detector that whitens hidden activations using within-class covariance and scores responses with a closed-form Fisher discriminant. Across Qwen-2.5-7B and Llama-3.1-8B on four QA datasets, DTS ranks first in five of eight settings and second in the remaining three. Whitening improves over cosine scoring by 7.8 AUROC points on average, identifying the readout as a major bottleneck. When truthful and hallucinated representations overlap, class-mean steering provides additional gains without learning a steering vector. DTS requires only a single forward pass and closed-form computation, making it substantially cheaper than sampling- and gradient-based alternatives, while also extending effectively to long-form generation.