From the link provided by Straybow in the other thread
The opinion makes it clear that there is no treaty until it has been ratified by congress - who may not do so. All this talk about States uppholding treaty obligations is therefore just flummery.
The Court upheld the rulings of the Texas Court of Criminal Appeals in a 6-3 opinion written by Chief Justice John G. Roberts. The Court held that the signed Protocol of the Vienna Convention did not make the treaty self-executing and, therefore, the treaty is not binding upon state courts until it is enacted into law by Congress. Furthermore, Chief Justice Roberts characterized the presidential memorandum as an attempt by the executive branch to enforce a non-self executing treaty without the necessary Congressional action, giving it no binding authority on state courts. Justice John Paul Stevens concurred in the opinion and Justice Stephen Breyer, joined by Justices David Souter and Ruth Bader Ginsburg, authored a dissent.
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