According to what would appear to have to be a very high source cultivated by New Focus International, sometime in early 2013 (i.e., in the aftermath of the satellite launch, or maybe the 3rd nuclear test) Jang Song-taek wrote “the Chinese leadership” a letter explaining he wanted to reform North Korea’s economy and rebalance the DPRK’s locus of power away from the Party and into the Cabinet.
The text of the letter (presumably read over the phone by New Focus’ source, or written down by someone extremely reckless and brought out by hand) described Jang’s view that North Korea had moved away from its administrative fundamentals established by Kim Il-sung.
Jang Song-taek’s alleged letter, coincidentally, works perfectly in keeping with New Focus International‘s historical interpretation of the 1980s (as described in the book Dear Leader), complaining that “following Kim Jong-il’s rise to power through the Party since the 80s, the country has functioned as a KWP-pivoted system.”
Is this enough to get a top official executed in North Korea? Perhaps. We aren’t supposed to ask questions about the way the system works, particularly when the questions or dirty laundry are being shared directly with unnamed Chinese counterparts.
According to New Focus, the main problem was that Kim Jong-un had given his uncle some leeway to approach Chinese leaders with this indecent proposal, suggesting again that the new leader’s diplomatic acumen and understanding of the system over which he presides was not very high.
During the “four day investigation” of Jang’s wrongdoing by the Ministry of State Security, Jang was said to repeatedly state that “the contents of the letter had not only had the approval of Kim Jong-un himself but his active support.” Thus the need for summary execution — leaving reformist impulses in the grave with Jang, and not implicating the new Supreme Leader.
While a few other details exist that bear discussion (the role of the Sinuiju SEZ, impact of the rumours domestically, ongoing crackdowns, partial confirmation of the story via the 13 December execution document, to name four), it seems that this story adds rather more weight than New Focus has done previously on the scenario of a powerless or at the very least, conflicted and ineffective, Kim Jong-un.
Adam Cathcart 
Yes, of course Jang would write a letter and note his criticism down on paper. Are we really supposed to believe this? One day either NFI will be vindicated or these stories will be proven wrong.
People write letters, plans, blueprints, memoranda etc. Big changes in political and administrative structures cannot be carried out without arguments on paper, while sounding out the leadership of an important neighbouring country would also be necessary. The existence of the letter has not been proved, but there is nothing illogical in the claims of NFI.