The term 'arbitrarily fine' can be broken down into three crossword solutions: 'AMERCE' (6 letters), 'amerces' (7 letters), and 'INJECT' (6 letters). 'AMERCE' is a verb meaning to impose a fine or penalty on someone, while 'amerces' is the third-person singular form of the same verb. 'INJECT' is a verb meaning to introduce something into a system or environment. Together, these words suggest that a fine is being imposed on someone in an arbitrary manner.