Which document must a pilot carry that proves they are qualified to operate the aircraft?

The document that a pilot must carry to prove they are qualified to operate an aircraft is the pilot certificate. This certificate indicates that the pilot has completed the necessary training and testing to legally fly certain types of aircraft, based on the classifications and ratings included in their certificate. It serves as a legal credential affirming the pilot has met the Federal Aviation Administration's (FAA) requirements regarding knowledge, skills, and competencies essential for safe aircraft operation.

Each of the other options serves a different purpose. The aircraft registration is essential for identifying and confirming the ownership of the aircraft but does not pertain to the pilot’s qualifications. A flight plan is used for filing intended flight routes with air traffic control, which helps manage air traffic and ensure safety; however, it does not establish pilot proficiency. The weight and balance report is crucial for operational safety, providing information to ensure the aircraft is loaded correctly, but it is not related to the pilot’s qualifications. Therefore, possessing a valid pilot certificate is the key requirement that affirms a pilot's ability to command an aircraft legally.