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While large language models (LLMs) have demonstrated remarkable abilities across various fields, hallucination remains a significant challenge. Recent studies have explored hallucinations through the lens of internal representations, proposing mechanisms to decipher LLMs' adherence to facts. However, these approaches often fail to generalize to out-of-distribution data, leading to concerns about whether internal representation patterns reflect fundamental factual awareness, or only overfit spurious correlations on the specific datasets. In this work, we investigate whether a universal truthfulness hyperplane that distinguishes the model's factually correct and incorrect outputs exists within the model. To this end, we scale up the number of training datasets and conduct an extensive evaluation -- we train the truthfulness hyperplane on a diverse collection of over 40 datasets and examine its cross-task, cross-domain, and in-domain generalization. Our results indicate that increasing the diversity of the training datasets significantly enhances the performance in all scenarios, while the volume of data samples plays a less critical role. This finding supports the optimistic hypothesis that a universal truthfulness hyperplane may indeed exist within the model, offering promising directions for future research.