How to Simulate a Stable Sort Cursor in Python

```python
import random

class CursorStableSortMock:
    """Simulates stable sorting with a cursor-like pointer for MongoDB-style queries."""
    
    def __init__(self, data, sort_key, reverse=False):
        self.data = list(data)
        self.sort_key = sort_key
        self.reverse = reverse
        self._index = 0
        self._stable_sort()
    
    def _stable_sort(self):
        """Perform stable sort maintaining original order of equal elements."""
        indexed_data = list(enumerate(self.data))
        indexed_data.sort(key=lambda x: x[0], reverse=False)  # preserve original indices
            
        # Stable sort by key using sorting by (key, original_index)
        indexed_data.sort(
            key=lambda x: (x[1][self.sort_key], x[0]),
            reverse=self.reverse
        )
        self.data = [item for _, item in indexed_data]
    
    def next(self):
        """Return next item from cursor or None if exhausted."""
        if self._index >= len(self.data):
            return None
        result = self.data[self._index]
        self._index += 1
        return result
    
    def rewind(self):
        """Reset cursor to beginning."""
        self._index = 0


if __name__ == "__main__":
    test_data = [
        {"name": "alice", "score": 85},
        {"name": "bob", "score": 92},
        {"name": "carol", "score": 85},
        {"name": "dave", "score": 92},
        {"name": "eve", "score": 70},
    ]
    
    cursor = CursorStableSortMock(test_data, sort_key="score", reverse=True)
    
    while True:
        item = cursor.next()
        if item is None:
            break
        print(f"{item['name']}: {item['score']}")
    
    # Demonstrate cursor rewind
    cursor.rewind()
    first_item = cursor.next()
    print(f"\nFirst item after rewind: {first_item['name']}: {first_item['score']}")