It's not that hard to prove that you did the work and not an AI. Show your work. Explain to the teacher why you wrote what you did, why that particular approach to the narrative appealed to you and you chose that as the basis for your work. Show an outline on which the paper was based. Show rough drafts. Explain how you revised the work, where you found your references, and why you retained some sources in the paper and not others.
To wit, show the teacher that YOU did the work and not someone else. If the teacher is not willing to do this with every student they accuse of malfeasance, they need to find another job. They're lazy as hell and suck at teaching.
Computer, show "my" work and explain to the teacher why "I" wrote what "I" did, describe why that particular approach to the narrative appealed to "me" and "I" chose that as the basis of "my" work. Produce an outline on which the paper could have been based and possible rough drafts, then explain how I could have revised the work to produce the final result.
And if you do all of that, and memorize it well enough to have an in-person debate with the teacher over whether or not you did the work, then maybe that's close enough to actually doing the work?
To wit, show the teacher that YOU did the work and not someone else. If the teacher is not willing to do this with every student they accuse of malfeasance, they need to find another job. They're lazy as hell and suck at teaching.