SelfCheck-Eval: A multi-module framework for zero-resource hallucination detection in large language models

Large language models (LLMs) have achieved considerable progress across diverse applications, yet their tendency to generate incorrect or fabricated content, commonly termed hallucinations, remains a fundamental obstacle to reliable deployment in high-stakes domains. Existing detection benchmarks are confined to general-knowledge settings, leaving specialized fields, where accuracy is important, underexplored. To address this gap, we introduce the American Invitational Mathematics Examination (AIME) Math Hallucination dataset, a benchmark for evaluating mathematical reasoning hallucinations, and propose SelfCheck-Eval, an LLM-agnostic, black-box detection framework compatible with open- and closed-source LLMs. The framework integrates three independent modules, semantic, specialized detection, and contextual consistency, into a suitable architecture. Systematic evaluation reveals a noticeable performance gap: existing methods perform well on biographical content but struggle with mathematical reasoning, a deficit that continues across natural language inference (NLI) fine-tuning, preference learning, and process supervision paradigms. These findings expose fundamental limitations of current approaches and motivate the development of specialized, black-box-compatible methods for trustworthy LLM deployment.