/ Paper arXiv 2610.39341
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Frontier language models such as GPT 6 Astra have contributed to research mathematics, demonstrating substantial reasoning capabilities. Yet serious reasoning failures persist even in tasks governed by explicit rules. We demonstrate this in retrograde chess which is a playground for pure reasoning, where solvers reconstruct legal histories and distinguish possible events from forced ones. We introduce RetroChessBench, a 12-task benchmark covering exact-length constructions, unique endings, and exhaustive answer sets, with references, rubrics, and a terminal-reward environment. In two trials per task and condition, GPT 6 Astra High fails to produce the required final answer in 22/24 attempts without tools and 18/24 with code execution; mean terminal RL rewards are 14.75% and 27.19%, respectively. The examples identify faulty deductions: failed responses reject legal histories and treat temporary obstructions as permanent. Online retrograde archives often provide puzzles and final move sequences without detailed derivations. We hypothesize that limited exposure to these missing explanations in web-derived training data contributes to the observed reasoning failures. This questions how far frontier mathematical reasoning really generalizes beyond familiar solution patterns. Claims of general intelligence require evidence that models can transfer learnt principles to areas with few worked examples.
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