This isn't like the four-color theorem. This is a computation that doesn't require any second-order logic. Beyond 7825, the induction is trivial for us humans, and we can let the computer halt. With only a finite amount of exact bead-pushing, what would such a question even mean? What could an answer to "why" be, except "I just showed you"?We don’t know what’s special about 7825 that would ruin everything.