They were guilty

Why execute them? Life imprisonment is punishment enough; after all, NO ONE else has been executed for espionage during peacetime by the US. THEY were executed because of the paranoia of the time, which was evilly exploited by the Honorable Scumbag of Wisconsin, Joe McCarthy, along with his Jewish, gay, ANTI-SEMITIC, HOMOPHOBIC rat, Roy Cohn. Look them up,then take a shower. Cohn in particular was a disgusting piece of work; I am convinced that if he lived in Germany during Hitler's reign, he would have turned in his fellow gay and Jewish citizens.

No proof except accusations by co-conspirators trying to save their own skins. Because the government could not release more conclusive proof like material from the Verona code project, the American public would have objected to more executions.