Does amending or supplementing a complaint to include new factual developments absolve the government of its burden to prove mootness?

QUESTION PRESENTED For two centuries, this Court has maintained the “timeof-filing” rule: “jurisdiction depending on the condition of the party is governed by that condition, as it was at the commencement of the suit.” E.g., Conolly v. Taylor, 27 U.S. 556, 565 (1829) (Marshall, C.J.); Lujan v. Defenders of Wildlife, 504 U.S. 555, 569 n.4 (1992). In contrast, courts analyze mid-litigation developments as matters of mootness. H.g., Ne. Fla. Chapter of Associated Gen. Contractors v. City of Jacksonville, 508 U.S. 656, 662 (1993). Petitioner Zachary Greenberg, a attorney, sued to enjoin enforcement of a speechregulating ethics rule. After the district court preliminarily enjoined enforcement of the rule, the government revised it and Greenberg supplemented his complaint to recount the new version of the rule. Applying the long-standing “time-of-filing” rule, the district court analyzed the mid-litigation developments— the revision of the rule and a disavowing declaration from one of the twelve defendants—as matters of mootness, finding neither mooted Greenberg’s challenge. App. 47a74a. The Third Circuit reversed, substituting a standing inquiry for a mootness one because Greenberg had amended his complaint to reflect the state’s mid-suit revision of the rule. App. 18a n.4. The question presented is: Does amending or supplementing a complaint to include new factual developments absolve the government of its burden to prove mootness?