BY EVAN RAMSTAD

SEOUL—As North Korea on Tuesday marks one month since the death of Kim Jong Il, the most important question for outsiders trying to deal with the country remains unanswered: Is his young son Kim Jong Eun really in charge?

North Korea has projected an image of a successful transition and stability in its authoritarian government. State media calls the younger Mr. Kim "supreme commander" and produced TV and newspaper reports praising him. It reported several visits he made to military installations and cultural events.

But the regime's New Year's statement, a lengthy message that traditionally contained an exhortation from Kim ...