Silver Spoon/WMG

The Gym Teacher is descended from an alternate universe version of Major Armstrong
One that fought in World War II and is famed for punching out his enemies.

Yugo's nightmare about getting paid the wrong way is a foreshadowing of something much more pleasant.
Just replace the calf with Aki, and there you have it. The dialogue doesn't even have to change!
 * Jossed. They gave him a check/cheque.

This universe is the one
We may meet Grand/Great grandchildren at some point in the story, and they will be friends of Hachiken's in either the present or the past. They will also be very good at science. Also, in this universe,  failed their attempt to   and change the course of history, which is why this version of Japan is just like ours.