What is the current state of the law on the test for establishing a conspiracy?

The supplemental instruction was neither erroneous nor prejudicial. The district court was correct as a matter of law to charge that the government needed only to prove agreement on one of the objectives charged in the indictment in order to establish that a conspiracy existed. See United States v. Papadakis, 510 F.2d 287, 297 (2d Cir. 1975). Of course, in order to obtain a conviction, the government also had to show that each defendant knowingly participated in a scheme to achieve this particular goal, see United States v. Washington, 48 F.3d 73, 80 (2d Cir. 1995), but the district court made this clear in both its original and supplemental instructions.