```python
def base_amount(amount: int, unit: str, defs: dict, base: str) -> int:
    if isinstance(amount, bool) or not isinstance(amount, int) or amount < 0:
        raise ValueError("amount must be a non-negative integer")
    if unit == base:
        return amount
    if unit not in defs:
        raise ValueError(f"unknown unit: {unit}")
    factor, finer = defs[unit]
    if not (isinstance(factor, int) and factor > 0):
        raise ValueError(f"bad factor for {unit}: {factor}")
    try:
        return base_amount(amount * factor, finer, defs, base)
    except RecursionError:
        raise ValueError("definition chain loops")
```