Which command authority is derived solely from a legislative provision or the President's order?

The correct choice is Combatant Command Authority, as it is the command authority that arises from formal legislative provisions or a direct order from the President of the United States. This authority encompasses the responsibility for the organized, trained, and equipped forces that are given the task of carrying out specific missions. Combatant Command Authority allows a commander to make decisions regarding the use of forces across a geographical or functional area and is crucial in military operations.

This type of authority is distinct because it is established through higher-level governance structures and legal frameworks, ensuring that military operations align with national defense policies and objectives as determined by legislative bodies and executive commands. In contrast, other command authorities, while important, do not derive solely from legislative provisions or presidential orders and often involve a range of responsibilities and control that could be tied to other factors, such as operational needs or administrative functions.