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README.md

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----
-dataset_info:
-  features:
-  - name: id
-    dtype: string
-  - name: category
-    dtype: string
-  - name: difficulty
-    dtype: string
-  - name: corrupted_code
-    dtype: string
-  - name: repair_target
-    dtype: string
-  - name: error_info
-    struct:
-    - name: correct_concept
-      dtype: string
-    - name: corrupted_concept
-      dtype: string
-    - name: error_type
-      dtype: string
-    - name: explanation
-      dtype: string
-  - name: domain_knowledge_required
-    sequence: string
-  - name: pwm_level
-    dtype: string
-  splits:
-  - name: train
-    num_bytes: 3482
-    num_examples: 7
-  - name: validation
-    num_bytes: 489
-    num_examples: 1
-  - name: test
-    num_bytes: 1519
-    num_examples: 3
-  download_size: 22586
-  dataset_size: 5490
-configs:
-- config_name: default
-  data_files:
-  - split: train
-    path: data/train-*
-  - split: validation
-    path: data/validation-*
-  - split: test
-    path: data/test-*
----
+# Quantum Lean Hard VVUQ Dataset
+
+## Overview
+This dataset contains challenging Lean 4 verification and repair problems designed to test advanced reasoning capabilities and demonstrate the effectiveness of Physics World Models (PWMs) in formal verification.
+
+## Problem Categories
+- **Type Theory**: 3 problems (coercion, dependent types, universes)
+- **Tactic Sequences**: 3 problems (wrong tactics, incorrect ordering)
+- **Proof Strategies**: 3 problems (wrong high-level approaches)
+- **Advanced Type Theory**: 1 problems (higher-order reasoning)
+- **Baseline**: 1 problems (simple for comparison)
+
+## Difficulty Distribution
+- Easy: 1 problems
+- Hard: 4 problems  
+- Expert: 6 problems
+
+## PWM Knowledge Levels
+- W1 (Basic): 1 problems
+- W2 (Intermediate): 3 problems
+- W3 (Advanced): 7 problems
+
+## Expected Performance
+- **Method A** (LLM only): Should struggle with hard/expert problems
+- **Method E** (LLM + W3): Should handle most problems successfully
+- **Clear gradient**: Performance should improve from A→B→C→D→E
+
+## Usage
+This dataset is designed for NeurIPS experiments demonstrating PWM effectiveness in formal verification tasks.
+
+## Requirements
+- Lean 4 with Mathlib
+- Enhanced diagnostics: `set_option diagnostics true`
+- Actual compilation verification (RequirementLEAN)