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Offline closed-loop Procedural Graph self-evolution operates across K rounds: (1) diagnostic rollout on training batch B_k collecting traces E_k; (2) feedback-driven mutation where an LLM refiner ingests tail-truncated trajectories C_k, task scores S_i^(k), and rejection history H_rejected to output structured JSON edits (add_nodes, delete_nodes, add_edges, delete_edges); (3) candidate preparation and structural checks (reaching terminal nodes with zero out-degree, cycle checks if disallowed); (4) validation gating where candidate G_k^cand is adopted if Sval(G_k^cand) >= Sval(G_k-1); and (5) rejection memory logging of failed candidates and diagnostics as negative evidence. · CiteArk