From the 4th Circuit motion:

Proceeding with the proposed cure process also poses a serious risk of irreparable harm directly to Justice Riggs by undermining the legitimacy of her election victory. The U.S. Supreme Court issued a stay in Bush v. Gore, forestalling various state-court remedies pending federal court review of the equal protection issues, because proceeding with a state process “of questionable legality” threatens irreparable harm to a candidate, as well as to the public, “by casting a cloud upon what [she] claims to be the legitimacy of [her] election.” 531 U.S. 1046, 1047 (2000) (mem.) (Scalia, J., concurring)….

Consistent with the Supreme Court’s issuance of a stay in Bush, federal courts across the country allow candidates for office to assert per se irreparable harm based on constitutional violations resulting from improper election challenges. See, e.g., Moore v. Circosta, 494 F. Supp. 3d 289, 321 (M.D.N.C. 2020); Jones v. United States Postal Serv., 488 F. Supp. 3d 103, 109, 139–40 (S.D.N.Y. 2020); Gallagher, 477 F. Supp. 3d at 26, 41–42. One can barely imagine the chaos that would ensue if an arbitrary, non-uniform, and constitutionally improper state-law “cure” process suggested a change to the election outcome, only for this Court later to decide that Justice Riggs’ constitutional arguments were meritorious and the “cure” process should never have proceeded. The proverbial toothpaste can never be put back in the tube, and that is exactly why the U.S. Supreme Court intervened in Bush v. Gore….

The challenged North Carolina voters were eligible to vote in November 2024, they followed every rule, and they acted in reliance on longstanding, unchallenged election laws. “Surely, upholding constitutional rights serves the public interest,” Newsom ex rel. Newsom v. Albemarle Cnty. Sch. Bd., 354 F.3d 249, 261 (4th Cir. 2003), especially when, as here, the threatened constitutional violation would erode the “fundamental” right to vote, Raleigh Wake Citizens Ass’n v. Wake Cnty. Bd. of Elections, 827 F.3d 333, 337 (4th Cir. 2016) (quoting Bush, 531 U.S. at 104–05). “Count first, and rule upon legality afterwards, is not a recipe for producing election results that have the public acceptance democratic stability requires.” Bush, 531 U.S. at 1047 (Scalia, J., concurring).

I had fleshed out such an argument earlier this week in my Slate piece.