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This paper argues that Lean verification of AI autoformalisation does not guarantee the correctness of the original natural-language proof, showing that semantically faithful translation is undecidable in the Solvability Complexity Index hierarchy. The authors demonstrate practical AI mistranslations, including a mismatch in OpenAI's announced Navier–Stokes blow-up proof.
The paper introduces a controlled benchmark for evaluating Large Language Models' robustness in step-level mathematical verification, revealing significant performance degradation on perturbed solution traces.