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metadata.json

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+{
+  "dataset_name": "quantum-lean-hard-vvuq-dataset",
+  "version": "1.0.0",
+  "description": "Hard Lean verification and repair dataset focusing on type theory, tactic sequences, and proof strategies",
+  "purpose": "Demonstrate Physics World Model (PWM) effectiveness in NeurIPS experiments",
+  "difficulty_levels": {
+    "easy": "Basic tactic completion",
+    "hard": "Complex reasoning required",
+    "expert": "Advanced type theory and proof strategies"
+  },
+  "categories": {
+    "type_theory": "Type coercion, dependent types, universe levels",
+    "tactic_sequence": "Incorrect tactic choices and ordering",
+    "proof_strategy": "Wrong high-level proof approaches",
+    "advanced_type_theory": "Higher-order reasoning patterns",
+    "baseline": "Simple problems for comparison"
+  },
+  "pwm_levels": {
+    "W1": "Basic Lean syntax and simple tactics",
+    "W2": "Intermediate proof patterns and mathematical reasoning",
+    "W3": "Advanced type theory and complex proof strategies"
+  },
+  "requirements": {
+    "RequirementLEAN": "All problems must be verified with actual Lean compilation",
+    "RequirementPWM": "Complete problem sets provided in prompts"
+  },
+  "expected_behavior": {
+    "Method_A": "Should fail on hard/expert problems",
+    "Method_E": "Should succeed with W3 knowledge",
+    "Differentiation": "Clear performance gradient across methods A-E"
+  }
+}