```python
def root_digit(value: int) -> int:
    """Fold a whole count down to a single figure by repeatedly summing its digits."""
    if value < 0:
        raise ValueError("value must be non-negative")
    if value == 0:
        return 0
    # Mathematical shortcut for digital root: 1 + (n - 1) % 9
    # This works for all positive integers.
    return 1 + (value - 1) % 9
```