Who gets to claim kids on taxes with 50/50 joint legal and physical custody?

My ex and I are currently in the middle of a divorce that started in September of '18. We have two children together and he was supposed to be paying child support since November when it was ordered. He's given me nothing for them to date. We both signed the custody agreement and we share joint legal and... show more My ex and I are currently in the middle of a divorce that started in September of '18. We have two children together and he was supposed to be paying child support since November when it was ordered. He's given me nothing for them to date. We both signed the custody agreement and we share joint legal and physical custody 50/50.

My question is, can I claim that I took care of the kids more than fifty percent of the time on our taxes because he hasn't been paying child support for more than half the year?

I make less than him, but I can claim Head of Household and get that credit, as well as the Child Tax Credit. He makes enough that he can't claim the child tax credit anymore. And he's very pigheaded. It's more than likely going to come down to which of us can efile faster with the irs. But is there a legal precedent for this?
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