Yes, this. The funding really works that way. The school district would get $4k from the state for a non-charter school student, and pony up $9k from other city funds. The charter school would get $13K from the state for a charter school student, and the state would give the city $13K less in aid (once the charter school has been around for 6 years. There's a bunch of transitional math that phases it in gradually, in the first 5 years.)

In the the end an elementary school's worth of students is projected to attend teh charter school rather than the public school, so the budget probably can't withstand losing an elementary-school's worth of budget (and then some) without closing an elementary school -- since they can't close a portion of each existing elementary school even if the numbers are just down proportionally throughout the system.