Probing Policy-Level Memorization in Reasoning LLMs via Atomic Chess

LLMs play chess at a notable level, but it is unclear whether this reflects memorization or rule-conditioned reasoning. We test this with atomic chess, a variant in which captures explode adjacent pieces, preserving notation but altering legal-move and terminal structure. We construct a paired benchmark of 200 variant-divergent positions from Lichess: 100 standard-source and 100 atomic-source positions, each selected so that the standard-best move is a severe blunder under atomic rules. On these positions, Claude Opus 4.6 and GPT-5.4 incur $2.1$--$4.6\times$ higher mean Win% loss under atomic than under standard rules on identical positions. Higher reasoning effort attenuates but does not close the gap; removing the rule statement collapses performance; and an unfiltered comparison shows the signal is hidden without prior-conflict filtering. Qualitative trace analysis reveals a recurring *unpropagated refutation* pattern: the model derives the correct atomic-rule consequence locally, then selects the move it just refuted. We argue this constitutes evidence of *policy-level memorization*, a behavioral signature complementary to extraction-based probes, and discuss implications for trust in instruction-following LLMs.