Michael H. answered 03/15/19
Ph.D. in mathematics and statistics; have taught at MIT and 8 others
"Gotten" is an older form of the past participle of "get". It parallels such verbs as "eat" and "give" and "fall", thus: "He eats.", "He ate." "He has eaten." or "He gives.", "He gave.", "He has given.", or "It falls.", "It fell.", "It has fallen." Similary "gets", "got", "has gotten".
But in England "gotten" seems to have largely disappeared before the 20th century, so "has got" is used instead of "has gotten". In America, "has gotten" is still used. But in America "He has got" means "He possesses" whereas "He has gotten" means "He has acquired."