```python
def flag_states(mask: int, catalog: list) -> dict:
    """Return a mapping of flag names to their boolean state based on the bit mask."""
    if not isinstance(mask, int) or isinstance(mask, bool):
        raise ValueError("mask must be an integer")
    if mask < 0:
        raise ValueError("mask must be non-negative")
    
    if not isinstance(catalog, list):
        raise ValueError("catalog must be a list")
    if len(catalog) == 0:
        raise ValueError("catalog must contain at least one name")
    
    seen_names = set()
    for name in catalog:
        if not isinstance(name, str):
            raise ValueError("flag name must be a string")
        if len(name) == 0:
            raise ValueError("flag name must be non-empty")
        if name in seen_names:
            raise ValueError("duplicate flag name in catalog")
        seen_names.add(name)
    
    num_flags = len(catalog)
    
    # Check if any bit at or beyond the catalog length is set
    # We need to check if mask has any bits set at positions >= num_flags
    # This is equivalent to checking if mask >= (1 << num_flags) is false? 
    # No, because mask could be large but have lower bits clear.
    # We need to check if (mask >> num_flags) is non-zero.
    if (mask >> num_flags) != 0:
        raise ValueError("mask has set bits at or beyond the catalog length")
    
    result = {}
    for i, name in enumerate(catalog):
        # Check if the i-th bit is set
        is_set = bool(mask & (1 << i))
        result[name] = is_set
        
    return result
```