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

Is Hadwiger's conjecture true?

Is Beal's conjecture true?

Is the Unique Games Conjecture true?

Is Szymanski's conjecture true?

Kirti-Mochizuki proof of the ABC conjecture is correct.

Is Haborth's Conjecture true?

Is Goodman's Conjecture true?

Is the 1/3–2/3 conjecture true?

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