Does Shinichi Mochizuki's proof of the abc conjecture include unfixable gaps?

Is the Unique Games Conjecture true?

Is the 1/3–2/3 conjecture true?

Kirti-Mochizuki proof of the ABC conjecture is correct.

Is Goodman's Conjecture true?

Is Haborth's Conjecture true?

Is Szymanski's conjecture true?

Conditional on Goldbach's conjecture being false, is Oldbach's conjecture true?

Is Hadwiger's conjecture true?

Is Beal's conjecture true?