The battle between Abigail Noel Fisher and the University of Texas at Austin continues with opposing views about where the case should go next.

In the past week, both sides filed replies in the U.S. 5th Circuit Court of Appeals. In those replies, filed July 29 by UT, and Aug. 1 by Fisher, the two sides each responded to each other’s arguments about where the U.S. Supreme Court, when on June 24 it remanded Fisher v. UT to the circuit court, intended for the potentially precedent-setting affirmative action litigation to land.

The options areto the appellate court for a ruling on the constitutionality of UT’s admissions policy, or to the district court for further development of the evidentiary record.

Fisher, a white woman who was rejected after applying to UT in 2008, alleged that the school violated her constitutional rights by using race as a factor in in its admissions process. The federal district court granted summary judgment in favor of the university.

On June 24, the Supreme Court vacated the 5th Circuit’s 2011 decision that upheld the school’s use of race as a factor in admissions. Justice Anthony Kennedy wrote for the 7-1 majority that the 5th Circuit “did not hold the University to the demanding burden of strict scrutiny articulated” in previous court decisions as governing race-based admissions.

In the June 24 order, the high court wrote: . . . [T]he case is remanded to the United States Court of Appeals for the Fifth Circuit for further proceedings consistent with the opinion of this Court,” and noted that Fisher recover $21,865.01 for the costs of printing of the record and the clerk costs.

In its July 29 reply concerning further proceedings on remand, UT defendants argue: ” . . . [G]etting the benefit of the District Court’s analysis would only aid this Court in reassessing the case. . . . Having the District Court reconsider the case in no way prevents this Court from doing so. To the contrary, it would put this Court in a better position to do so because an appellate court always benefits from having the lower court’s analysis in taking up an issue.”

But in contrast, in her appellant’s reply in support of proposed schedule for supplemental briefing, Fisher argues: “The Court should reject Appellee University of Texas’s (‘UT’) proposal to extend and expand the remand proceedings. Appellant proposed supplemental briefing to ensure fairness to all parties under a schedule ensuring prompt resolution of a case that now has been pending for over five years.”

The high court did not explicitly say that the case could return to the district court, therefore it should not, Fisher argues.

“When the Supreme Court gives the court of appeals discretion to decide an issue itself or remand to the district court, it says so,” her reply states.

Bert Rein, a partner in the Washington office of Wiley Rein, who represents Fisher, declines to comment about the case, referring to the recent filing. Gregory Garre, a partner in the Washington office of Latham & Watkins, who represents UT and officials, didn’t immediately return a call to his office.

Gary Susswein, a spokesman for UT, writes in an email that the school will let its filings speak for themselves. But in response to a question about its lawyers, Susswein writes: “We have renewed Latham [&] Watkins’ contract for six months, after which we will reassess based on whether the case is continuing or has been resolved. We are paying them $250,000 for the next six months on top of the approximately $987,000 we have paid them to date.”