Fig. 6: Candidate reasoning trajectories generated by the MCTS-based generator.

For materials science queries, the generator explores multiple reasoning paths using Monte Carlo Tree Search (MCTS). Each trajectory represents a distinct sequence of reasoning actions (e.g., A3 → A3, A5 → A5, A4 → A5), composed of intermediate steps that collectively construct structured material–value–unit triples. All paths ultimately converge on the accurate extraction of key entities, such as CeO₂: 176.9 GPa; PrO₂: 176.9 GPa; and Th₀.₆Pr₀.₄O₂₋ₓ: 175 ± 12 GPa.