We introduce an intuitive method to test the robustness (stability and explainability) of any black-box LLM in real-time via its local deviation from harmoniticity, denoted as $γ$. To the best of our knowledge this is the first completely model-agnostic and unsupervised method of measuring the robustness of any given response from an LLM, based upon the model itself conforming to a purely mathematical standard. To show general application and immediacy of results, we measure $γ$ in 10 popular LLMs (ChatGPT, Claude-2.1, Claude3.0, GPT-4, GPT-4o, Smaug-72B, Mixtral-8x7B, Llama2-7B, Mistral-7B and MPT-7B) across thousands of queries in three objective domains: WebQA, ProgrammingQA, and TruthfulQA. Across all models and domains tested, human annotation confirms that $γ\to 0$ indicates trustworthiness, and conversely searching higher values of $γ$ easily exposes examples of hallucination, a fact that enables efficient adversarial prompt generation through stochastic gradient ascent in $γ$. The low-$γ$ leaders among the models in the respective domains are GPT-4o, GPT-4, and Smaug-72B, providing evidence that mid-size open-source models can win out against large commercial models.