Notice period paid or unpaid freelancer Japan

So I've been freelancing full-time for this company for a few months now.

My contract says either of us can terminate the contract with a one month written notice (nothing less, nothing more).

Boss gave me verbal notice a month ago but was very unclear whether or not it was official, and said he'll get back to me officially later, which he never did.

Today, he said that the notice period just ended and that he wasn't required to pay me for it because I'm a contractor. Then sent me the written notice on the same day. Should be noted that it's written absolutely nowhere in the contract that the notice period would be unpaid.

From what I get, I should be paid my notice period, otherwise what's even the point of it in the contract, he could just call me and say "Today's your last day, bye". Basically, I should stay available during the notice period in case he needs something, but I have no counterpart? Seems fishy to me.

I disputed it and he offered 50% of the month salary, which makes me think that he knows he's out of line (why would you offer me 50% if you know you legally don't have to give me a cent?)
His argument being that he didn't give me any tasks for the month. However, I'm not on a project based contract, my salary is fix every month, no matter the number of hours – lower activities shouldn't be my risk financially I feel.

Am I on the right track here? Or am I missing something? What should I do in that situation?

Accepting 50% wouldn't even cover my monthly expenses. (I know freelancing can be tricky but it was just for a few months as I'm leaving Japan eventually).

by Admirable_Piccolo260