TimeLitmus: A Diagnostic Benchmark for Cross-Modal Understanding and Explanation Faithfulness in Event-Conditioned Time-Series Prediction

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Large language models (LLMs) are increasingly used to make predictions from numerical time-series histories and textual events. Yet accuracy alone cannot reveal whether correct answers reflect effective integration of the two inputs or instead arise from event polarity, unimodal priors, or superficial cues. Likewise, plausible explanations may rationalize predictions without faithfully reflecting the evidence that drives model behavior. We introduce TimeLitmus, a diagnostic benchmark for cross-modal understanding and explanation faithfulness in event-conditioned time-series prediction. TimeLitmus contains 4,856 evaluation records across Finance and Traffic, combining natural prediction with controlled counterfactual and contrastive interventions, explanation-targeted faithfulness tests, and systematic shortcut controls. Across ten representative LLMs, standard prediction accuracy substantially overstates reliable cross-modal understanding: Hard Paired Contrast (HPC) pair correctness peaks at only 19.2% in Finance and 11.7% in Traffic, and all ten models show lower-than-expected consistency on Finance series-side controls. Models often recognize scenario relations explicitly yet fail to apply them during independent prediction. Explanation faithfulness shows a similar gap: in Traffic, most models cite the manipulated temporal factor in over 90% of cases, while behavioral support remains below 22%. Human annotators outperform LLMs on matched controlled and hard-pair diagnostics, confirming that these distinctions are recoverable from the inputs. Natural-only adaptation yields selective gains in evidence selection and input sensitivity, but not consistent gains in controlled or hard-pair behavior. The benchmark, evaluation suite, and supervised adaptation data will be released publicly.