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Recent deep learning methods for fMRI-based diagnosis have achieved promising accuracy by modeling functional connectivity networks. However, standard approaches often struggle with noisy interactions, and conventional post-hoc attribution methods may lack reliability, potentially highlighting dataset-specific artifacts. To address these challenges, we introduce PIME, an interpretable framework that bridges intrinsic interpretability with minimal-sufficient subgraph optimization by integrating prototype-based classification and consistency training with structural perturbations during learning. This encourages a structured latent space and enables Monte Carlo Tree Search (MCTS) under a prototype-consistent objective to extract compact minimal-sufficient explanatory subgraphs post-training. Experiments on three benchmark fMRI datasets demonstrate that PIME achieves state-of-the-art performance. Furthermore, by constraining the search space via learned prototypes, PIME identifies critical brain regions that are consistent with established neuroimaging findings. Stability analysis shows 90% reproducibility and consistent explanations across atlases.