Modern LLMs demonstrate impressive multilingual performance, yet standard benchmarks primarily reward selecting correct answers rather than evaluating genuine factual understanding. We introduce Systematic Wikidata-based Object-Relation Distortion (SWORD), a benchmark that evaluates whether models consistently reject factual errors across languages. SWORD generates syntactically well-formed but factually incorrect statements in eight widely spoken languages through controlled perturbations of Wikidata triples, ranging from random entity substitutions to semantically plausible property-based selections. Our distortion-based evaluation surfaces two critical insights that remain entirely obscured by conventional benchmarks. First, models counterintuitively achieve higher accuracy on semantically plausible distortions than on nonsensical random substitutions, suggesting reliance on distributional familiarity rather than genuine factual verification. Second, models exhibiting comparable baseline accuracy across languages show substantial performance degradation specifically on (East) Asian languages when presented with distorted statements, with cross-lingual performance gaps reaching up to 28 percentage points (49\% relative reduction) in some models. These findings demonstrate that multilingual factual reasoning involves asymmetric capabilities that aggregate accuracy metrics systematically obscure.

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