A federal appeals court in Boston heard arguments in a closely watched dispute over whether a district judge had the authority to order the restoration of more than $2.6 billion in research funding to Harvard after the Trump administration cut it off. The case places two recurring legal questions in sharp relief: how far the executive branch can go in withholding federal money, and how far courts can go in crafting remedies when they find that action unlawful.

At the center of the appeal is an order by U.S. District Judge Allison Burroughs restoring the funding, a remedy the administration argues exceeded the court’s power.