```python
def mean_window(readings: list, size: int) -> list:
    """Return the mean of every run of `size` consecutive readings, rounded down."""
    if size <= 0:
        raise ValueError("Window size must be a positive integer")
    if not readings:
        return []
    if size > len(readings):
        return []
    
    result = []
    for i in range(len(readings) - size + 1):
        window = readings[i:i + size]
        mean_val = sum(window) / size
        result.append(int(mean_val))
    return result
```