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 Id. at 1075. The parties then fully briefed the ultimate question of whether the district court erred in issuing the stay order. Over thirty amici filed separate briefs on various topics. Oral argument was held on May 17, 2023, in which each side was allowed forty minutes to present its argument, double the ordinary allotted time. We now consider the merits of the appeal.

Before considering the Medical Organizations and Doctors’ claims, we must determine whether they have standing to assert them; an injunction is always improper if the district court lacked jurisdiction. Cruz v. Abbott, 849 F.3d 594, 598–99 (5th Cir. 2017). At this stage, it is the plaintiffs’ burden to “make a ‘clear showing’ that they have standing to maintain the preliminary injunction.” Barber v. Bryant, 860 F.3d 345, 352 (5th Cir. 2017) (quoting Winter v. Nat. Res. Def. Council, Inc., 555 U.S. 7, 22 (2008)). And so the Medical Organizations and Doctors must satisfy the three basic elements of standing: injury, traceability, and redressability. Lujan v. Defs. of Wildlife, 504 U.S. 555, 560 (1992).

Standing in this appeal turns principally on the “injury” prong. The Medical Organizations and Doctors seek prospective relief, so they must establish future injury. To do that, they must show that “the threatened injury is ‘certainly impending,’ or there is a ‘substantial risk’ that the harm will occur.” Susan B. Anthony List v. Driehaus, 573 U.S. 149, 158 (2014) (quoting Clapper v. Amnesty Int’l USA, 568 U.S. 398, 414 n.5 (2013)). As those standards indicate, the plaintiffs must show that the threat of future injury is sufficiently likely. The Supreme Court has thus rejected standing theories that rely “on a highly attenuated chain of possibilities” or that “require guesswork as to how independent decisionmakers will exercise their judgment.” Clapper, 568 U.S. at 410, 413.

Even so, a “substantial risk” does not require that the threatened