One of several reasons that North Korea can get away with such bad behavior is that it receives crucial economic and political support from China. That's why the United States, which has few ways left to punish the rogue state, is trying to convince Beijing that the little client state is more trouble than its worth.

Since North Korea began its most recent round of provocations, there have been some real signs that China is increasingly frustrated with its misbehaving neighbor. Leader Xi Jinping gave a speech that made some thinly veiled criticisms of the North's outbursts, Chinese state media has been unusually critical of Pyongyang and there are some good signs that Chinese people themselves are fed up with Kim Jong Un and his regime.

It's looked like great news: China has real influence over North Korea, which relies deeply on Chinese trade and assistance. If China is so unhappy with Kim, then it stood to reason it  might reign him in by withdrawing, or threatening to withdraw, some of its support.

Alas, there is now a good sign that, for all China's tough rhetoric and evident impatience, the country might actually be deepening its economic ties with North Korea. China is constructing a massive, $356 million bridge over the Yalu river, which divides the two countries, in an effort to promote more cross-border trade, according to Bloomberg News. The bridge will be linked to a high-speed rail network connecting the North Korean border to several nearby Chinese cities. According to local Chinese officials and businessmen who spoke to Bloomberg, the recent political turmoil has not appreciably hurt trade.

Exports into North Korea from China totaled about $590 million last quarter, up 2.5 percent from the previous year. This is a crucial source of income for North Korea, which desperately needs all the hard currency it can get to keep its economy going. Chinese exports into North Korea were down in the same period, though, perhaps reflecting greater poverty among North Korean citizens. (Neither of these statistics includes the thriving black-market trade that moves across the border.)

Two weeks ago, some reports suggested that Dandong, the Chinese border city where this new bridge is going up, had closed the border to Chinese tourists. That shut-down would have curbed the inflow of Chinese cash into North Korea, potentially a punishment for Pyongyang's behavior. But those reports were never fully confirmed.

So why would China still support North Korea, despite all its recent misgivings? China's policy for the Korean peninsula can be summed up in six little words: "No war, no instability, no nukes." Those are Beijing's priorities, and in that order. Chinese leaders don't want nukes, which is why they're upset about Pyongyang's recent nuclear brinksmanship. But even more than that, they don't want the North Korean state to collapse into chaos or devolve into war, and they know that economic support and cross-border trade are good ways to maintain the status quo. And it's the status quo that China appears most interested in.