The software he patented — which he claimed, among other things, could find terrorist plots hidden in broadcasts of the Arab network Al Jazeera; identify terrorists from Predator drone videos; and detect noise from hostile submarines — prompted an international false alarm that led President George W. Bush to order airliners to turn around over the Atlantic Ocean in 2003.

The software led to dead ends in connection with a 2006 terrorism plot in Britain. And they were used by counterterrorism officials to respond to a bogus Somali terrorism plot on the day of President Obama’s inauguration, according to previously undisclosed documents…

C.I.A. officials, though, came to believe that Mr. Montgomery’s technology was fake in 2003, but their conclusions apparently were not relayed to the military’s Special Operations Command, which had contracted with his firm. In 2006, F.B.I. investigators were told by co-workers of Mr. Montgomery that he had repeatedly doctored test results at presentations for government officials. But Mr. Montgomery still landed more business.

In 2009, the Air Force approved a $3 million deal for his technology, even though a contracting officer acknowledged that other agencies were skeptical about the software, according to e-mails obtained by The New York Times.