{
  "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"
  }
}