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Yea, Boumediene! If pushed, the Supreme Court only has to connect the dots now for Afghanistan. They ruled already that Common Article 3 applies always (Hamdan), and in Boumediene they said any court that could not free a prisoner was not a valid judicial venue for habeas corpus pleas.
All that's left is to rule that the judicial review guaranteed in CA3 and Article 5 includes habeas corpus.
CA3 prohibits: "(d) the passing of sentences and the carrying out of executions without previous judgment pronounced by a regularly constituted court, affording all the judicial guarantees which are recognized as indispensable by civilized peoples."
And Article 5 requires: "Should any doubt arise as to whether persons, having committed a belligerent act and having fallen into the hands of the enemy, belong to any of the categories enumerated in Article 4, such persons shall enjoy the protection of the present Convention until such time as their status has been determined by a competent tribunal."