I had resolved myself to the idea that we might not prove our theorem in full generality. I accepted that we’d settle for writing a paper where we made a conjecture about the general case and wrote proofs for, I don’t know, up through n = 6 or something.
Note-to-Gibbons: You shouldn’t doubt your incredible REU group like that! We riffed on the general ideas in our proof and about 10 minutes ago, we proved the general case!
Now, I know it’s dangerous to declare that you have a proof right after coming up with it. However, it’s important to celebrate immediately after proving something just in case it isn’t an actual proof. Pro tip: this technique will maximize your personal happiness in the field of mathematics.
But the best part of all of it is that I don’t have to write any more code!