He would not go into detail about the methods in order to prevent the attack being used on real victims but said a proof-of-concept attack had been developed at the university.
Given the enormous computing resources that would be required to solve it, some scientists say a proof will not come for a century.
"Final proof," said a cartoon in Tages Anzeiger depicting a starry sky.
The Pentagon official said a higher standard of proof was required before this clearance could be revoked, partly, he said, because it affected Mr. Deutch's livelihood.
"As far as I know, the Pakistanis are saying this is it, this is the proof," said a senior State Department official, who, like other officials contacted for this article, spoke on condition of anonymity because of the continuing investigation.
"If you go in there and speak Spanish, they give you a big hassle and want to see all kinds of proof," said a welder from Mexico in Spartanburg, S.C., who crossed over illegally.
He said a culture of "wanting proof" of faith and proselytizing has increased the fervor around near-death stories.
"I'm living in a safe area, very strong, earthquake-proof," said a successful middle-class professional in his 30s.
Where Heyting says that a proof of ¬a establishes a reduction of the solution of any problem to that of a, Kolmogorov had said that it established that the problem of reducing the solution of any problem to that of a has become without content.
Havasi says as a proof of concept they have been working with Sony compiling information from social media about people's reaction to the World Cup as it happens.
A refutation, Aristotle says, is "a proof of the contradictory" (SR 6, 168a37)—a proof of the proposition which is the contradictory of the thesis maintained by the answerer.
