After each North Korean provocation, a soothing mantra echoes through the halls of government and think tanks in the United States.

China, it is frequently said, could solve this seemingly unsolvable problem, finally reining in North Korea, if Beijing were just properly motivated.

But this oft-repeated line contains three assumptions, none of which has held up well in recent years.

It assumes that outside pressure could persuade North Korea to curtail or abandon its weapons programs. That China has the means to bring about such pressure. And that Beijing will do so once it is properly cajoled or coerced.