```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")
    
    def walk_units(current_unit, current_amount):
        # Check if the current unit is the base
        if current_unit == base:
            return current_amount
        
        # Check if the current unit is defined
        if current_unit not in defs:
            raise ValueError(f"Unit '{current_unit}' is not defined")
        
        factor, finer = defs[current_unit]
        
        # Check if the factor is a positive integer
        if not isinstance(factor, int) or factor <= 0:
            raise ValueError("Factor must be a positive integer")
        
        # Calculate the amount in the finer unit
        return walk_units(finer, current_amount * factor)
    
    try:
        return walk_units(unit, amount)
    except ValueError as e:
        raise ValueError(f"Error converting amount: {e}")
```

This implementation defines a helper function `walk_units` to recursively multiply the amount by the factor of the finer unit until it reaches the base unit. It also includes checks for non-negative integers, undefined units, negative factors, and loops in the definition chain.