```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 neither defined nor the base unit.")
    if defs.get(unit, [0])[0] <= 0:
        raise ValueError("Factor for a unit must be a positive whole number.")

    while unit != base:
        factor, finer = defs[unit]
        amount *= factor
        unit = finer

    return amount
```