```python
def base_amount(amount: int, unit: str, defs: dict, base: str) -> int:
    if amount < 0 or not isinstance(amount, int):
        raise ValueError("Amount must be a non-negative whole number")
    if unit not in defs and unit != base:
        raise ValueError(f"Unit {unit} is not defined or the base unit")
    if any(factor <= 0 for factor, _ in defs.values()):
        raise ValueError("Factor must be a positive whole number")
    
    while unit != base:
        factor, finer = defs[unit]
        amount *= factor
        unit = finer
    
    return amount
```