Use revision control and frequently commit your work, preferably along with comments describing your thinking process. In law school I used Git as that's what I was familiar with and it made it easy to backup my work (git push), but I suppose the tracking feature in MS Word might suffice.
In law school you cite almost every sentence in a written work. In theory you don't need to cite your own, bare opinions, but even then it's common to provide citations for rhetorical effect. And legal citations are very specific and descriptive, which is why footnotes are often so long. Rigorous citation is just a good idea in any field, and they're more costly to fake, at least if they're more than just last name & year. (If you're playing a long game, make sure archive.org has a snapshot of any online sources; they provide browser extensions for that.)
It also might not be a bad idea to capture your browsing history, so you can show a timeline of how your research went. In law school this history is already captured by the legal portals as part of their billing system, but standard browsing history would be more than sufficient.
Finally, and perhaps most importantly, if you do any of this, then be consistent. Don't do this for one class but not another, or have browsing history for some papers but not others. Consistency speaks to both credibility and reliability of evidence. So it's better to have no browsing history for any than only for some. A professor in a Wills & Trust class explained it this way: one day you'll be presented with a document you helped execute 30 years ago and asked, for example, if the identities of witness signatures were verified. You'll have no direct recollection of this. But you could answer in the affirmative; you could say, "Yes, because whenever executing a document I always did X, Y, and Z, without fail." (Or alternatively, "I almost always did X, Y, and Z, and the rare exceptions are memorable".) And if you indeed were consistent about this, there'll be corroborating evidence. So if someone is skeptical about whether your Git version history was authentic, you want to be able to point them to version histories for all your most recent papers as corroborating your process.
Type your work in a Google Doc with edit history enabled. Or if you're writing code, push signed commits to a repository shared with your professor, every few hours you're working on it. Honestly, even for essays, maybe share the Google Doc with your professor ahead of time. It might annoy them but at least you're covering your bases early.
Alternatively: write about controversial topics and/or fill your paper with obscenities :)
Do what the exonerated student did - use the track changes feature in your word processor. I would think something like Github and some simple tools (so a non programmer could use easily) to provide basic version control would be a good way to track versions and time stamps of updates to docs, projects, etc.
The cynic in me says that human student papers will stand out for being badly written, while the ChatGPT cheaters will have more superficial polish (if less solid reasoning).
In law school you cite almost every sentence in a written work. In theory you don't need to cite your own, bare opinions, but even then it's common to provide citations for rhetorical effect. And legal citations are very specific and descriptive, which is why footnotes are often so long. Rigorous citation is just a good idea in any field, and they're more costly to fake, at least if they're more than just last name & year. (If you're playing a long game, make sure archive.org has a snapshot of any online sources; they provide browser extensions for that.)
It also might not be a bad idea to capture your browsing history, so you can show a timeline of how your research went. In law school this history is already captured by the legal portals as part of their billing system, but standard browsing history would be more than sufficient.
Finally, and perhaps most importantly, if you do any of this, then be consistent. Don't do this for one class but not another, or have browsing history for some papers but not others. Consistency speaks to both credibility and reliability of evidence. So it's better to have no browsing history for any than only for some. A professor in a Wills & Trust class explained it this way: one day you'll be presented with a document you helped execute 30 years ago and asked, for example, if the identities of witness signatures were verified. You'll have no direct recollection of this. But you could answer in the affirmative; you could say, "Yes, because whenever executing a document I always did X, Y, and Z, without fail." (Or alternatively, "I almost always did X, Y, and Z, and the rare exceptions are memorable".) And if you indeed were consistent about this, there'll be corroborating evidence. So if someone is skeptical about whether your Git version history was authentic, you want to be able to point them to version histories for all your most recent papers as corroborating your process.