{ "trace_summary": { "theorem_name": "intro_apply", "status": "verified", "n_steps": 4, "n_unique_goal_states": 1, "n_flexure_joints": 4 }, "spectral": { "n_states": 1, "eigenvalue_max": 4.0, "spectral_gap": 4.0, "laplacian_eigenvalue_max": 4.0, "rank_estimate": 1, "zero_rows": 0, "frobenius_norm": 4.0, "trace": 4, "density": 4.0 }, "feature_vector": [ 4, 1, 4.0, 4.0, 0, 1, 0.0, 0.0, 0.0, 1.0, 0.25, 4532 ], "feature_names": [ "n_steps", "n_unique_goal_states", "transition_density", "spectral_gap", "laplacian_zero_count", "rank_estimate", "avg_delta_goal_count", "avg_delta_hypothesis", "avg_delta_symbol", "tactic_family_entropy", "verified_ratio", "total_elapsed" ], "tactic_family_distribution": { "introduction": 2, "discharge": 2 }, "delta_stats": { "avg_goal_delta": 0.0, "avg_hypothesis_delta": 0.0, "avg_symbol_delta": 0.0, "max_delta_score": 0 }, "flexure_joints": [ { "step": 0, "tactic": "intro h", "tactic_family": "introduction", "delta_score": 0, "delta": { "symbol_delta": 0, "hypothesis_delta": 0, "goal_count_delta": 0 }, "result": "failure" }, { "step": 1, "tactic": "intro hA", "tactic_family": "introduction", "delta_score": 0, "delta": { "symbol_delta": 0, "hypothesis_delta": 0, "goal_count_delta": 0 }, "result": "failure" }, { "step": 2, "tactic": "apply h", "tactic_family": "discharge", "delta_score": 0, "delta": { "symbol_delta": 0, "hypothesis_delta": 0, "goal_count_delta": 0 }, "result": "failure" }, { "step": 3, "tactic": "exact hA", "tactic_family": "discharge", "delta_score": 0, "delta": { "symbol_delta": 0, "hypothesis_delta": 0, "goal_count_delta": 0 }, "result": "success" } ] }