School district attorney Alan Rupe, left, presents his case in a school funding case at the Kansas Supreme Court Wednesday, Sept. 21, 2016, in Topeka, Kan. The hearing stems from a 2010 lawsuit brought by four school districts contending schools are underfunded by the state. (AP Photo/Charlie Riedel)

Topeka ? Attorneys in the long-running school finance lawsuit on Friday delivered their final written arguments to the Kansas Supreme Court on why the additional money that lawmakers approved for public schools this year either should or should not be upheld as constitutional.

The court’s ruling in the case will determine whether public schools can open as scheduled in August, or whether lawmakers will be forced back into a special session this summer to correct any further constitutional flaws.

The briefs filed with the court on Friday are each party’s response to the other side’s initial arguments, which were filed last week.

After debating school finance issues for most of the 2017 session, lawmakers finally settled on a bill in June that reinstates a per-pupil funding formula similar to the one they repealed in 2015 and provided for an additional $194.7 million in funding for the upcoming school year, plus another $97.8 million on top of that in the following school year.

Gov. Sam Brownback, who had largely stayed out of the school finance debate throughout the session, signed the bill on June 15, although he criticized it, saying lawmakers, “missed an opportunity to substantially improve the K-12 funding system.”

Brownback had signaled earlier that he wanted to see more “school choice” programs such as charter schools or vouchers to pay for private school tuition.

However, he also acknowledged that the bill directs more funding into “classroom” spending by limiting the amount of state money spent on bond and interest payments.

Attorneys for the state argued that the new law should be upheld because it directs more money for programs that help “at-risk” students than the amount that the court said was constitutionally sufficient in the previous school finance case in 2005.

In their response, however, attorneys for the plaintiffs said that was “demonstrably false,” and that the amount of at-risk funding in the new law is actually $74 million less than what a Legislative Post Audit study had recommended for 2007.

In their initial brief last week, the plaintiffs argued that the base per-pupil funding amount of $4,006 in the new law is far short of what the Kansas State Board of Education had recommended in its budget request, or of what the three-judge trial court panel had ordered in its initial ruling in the case in 2013.

In its response filed Friday, though, the state argued that base per-pupil aid, by itself, has never been used as the standard for deciding whether overall funding is constitutionally adequate.

The Kansas Legislature, through its special counsel, former State Sen. Jeff King, also filed a brief last week arguing that the new law should be upheld as constitutional, explaining in detail how the Legislature arrived at the amounts included in the new law.