> It's sufficient for Mochizuki. Everyone else can decide for themselves

This sounds like a variant of the Turing test.

Mochizuki and your pet dog both claim to have proven the ABC conjecture. The ABC conjecture has been proven when you can understand one proof but not the other.

I love your idea in principle, but it would be very problematic, and very sensitive to the tester's prior experience. I think that many people would (un)naturally be more trustful of mathematically-looking squiggles than a dog's barks, while others, especially if they got burned by damn lies before, would inherently distrust mathematics. In any case, people are very prone to trying to complete gaps in their understanding of a speaker based on prior conceptions.

I can't edit my post, but I should have phrased it more pithily:

Mochizuki and your pet dog both claim to have proven the ABC conjecture. The ABC conjecture has been proven when you can tell the difference between the two proofs.

Presumably he’d like recognition for having proven it. Unless he can explain and communicate his theorem to others, his work won’t be accepted. That doesn’t seem sufficient.