```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 a non-negative integer")
    if mask < 0:
        raise ValueError("mask must be a non-negative integer")
    
    if not isinstance(catalog, list):
        raise ValueError("catalog must be a list")
    if len(catalog) == 0:
        raise ValueError("catalog must hold at least one name")
    
    seen_names = set()
    for name in catalog:
        if not isinstance(name, str):
            raise ValueError("flag name must be a non-empty string")
        if len(name) == 0:
            raise ValueError("flag name must be a non-empty string")
        if name in seen_names:
            raise ValueError("repeated flag name")
        seen_names.add(name)
    
    num_flags = len(catalog)
    
    # Check if any bit at or beyond the catalog's 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 not quite right
    # because we only care about bits at positions >= num_flags being 0.
    # Actually, if mask has a bit set at position i where i >= num_flags, it's invalid.
    # So we need to ensure that all bits from num_flags upwards are 0.
    # This means mask must be less than 2^num_flags.
    if mask >= (1 << num_flags):
        raise ValueError("mask has a set bit at or beyond the catalog's 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
```