In an appalling 5-to-4 ruling on Thursday, the Supreme Court’s conservative majority tossed aside compelling due process claims, the demands of justice and a considered decision by a lower federal appeals court to deny the right of prisoners to obtain post-conviction DNA testing that might prove their innocence.

The inmate at the center of the case, William G. Osborne, is in prison in Alaska after a 1994 rape conviction based in part on a DNA test of semen from a condom recovered at the scene.

The state used an old method, known as DQ-alpha testing, that could not identify, with great specificity, the person to whom the DNA belonged. The high court sided with Alaska in its refusal to grant Mr. Osborne access to the physical evidence, the semen. His intent was to obtain a more advanced DNA test that was not available at the time of his trial and that prosecutors agreed could almost definitively prove his guilt or innocence.

Writing for the majority, Chief Justice John G. Roberts Jr. noted the “unparalleled ability” to prove guilt or innocence using DNA evidence. But he treated that breakthrough more as an irritant than an opportunity.