```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")
    
    visited = set()
    
    while unit != base:
        if unit in visited:
            raise ValueError("loop detected in definition chain")
        visited.add(unit)
        
        if unit not in defs:
            raise ValueError(f"unknown unit: {unit}")
        
        factor, finer = defs[unit]
        if not isinstance(factor, int) or factor <= 0:
            raise ValueError(f"bad factor for unit {unit}: {factor}")
        
        amount *= factor
        unit = finer
    
    return amount
```