A fact from Yongle Emperor's campaigns against the Mongols appeared on Wikipedia's Main Page in the Did you know column on 21 January 2014 (check views). The text of the entry was as follows:
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During the early 15th century (the reign of Yongle Emperor), the Eastern Mongols were basically under the rule of a united political entity, known as the Post-Imperial Mongolia or the Northern Yuan dynasty. The Ming was fighting against groups of the Eastern Mongols under the rule of the Post-Imperial Mongolia. In WP it is conventional to list the actual political entity that is involved, which is the Post-Imperial Mongolia, where Eastern Mongols were ruled by it. Eastern Mongols is currently a disambiguation page in WP, which in the usage of this term in this article refers to groups of Mongols under the Post-Imperial Mongolia. It's much more informative to link to the article Post-Imperial Mongolia, which discussed in detailed about the Mongols under its rule and its relationship with Ming China. --Cartakes (talk) 23:35, 1 August 2015 (UTC)[reply]
That is under the presumption that the conflict was Ming against a united political entity. The conflict was in fact not against an united political entity, but against several divided entities. Some of which took advantage of the situation to further themselves against one another. Specificity about the actual combatants is needed here, reflective of the usage in sources. You may feel to note the who-and-who is a ruler of something in name, but the actual combatants involved is still different. --Cold Season (talk) 23:49, 1 August 2015 (UTC)[reply]
I was only talking about Eastern Mongols under the Post-Imperial Mongolia obviously. There were Western Mongols or Oirats and other smaller Mongol tribes involved of course, which were also fighting with the Ming. There was no single united *Mongol* political entity obviously, but the Eastern Mongols were under the Post-Imperial Mongolia. Furthermore, if you look at the Chinese version of the article[1], which lists "鞑靼、瓦剌" as opponents to the Ming. "鞑靼、瓦剌" corresponds to the Post-Imperial Mongolia and the Oirats in English. --Cartakes (talk) 00:00, 2 August 2015 (UTC)[reply]
I just see a lack of sources at zh.wiki, which is what I find rather unreliable to go by. In the sources (including those given here), they specify and use the term Eastern Mongols. Post-Imperial Mongolia is broad, Eastern Mongols is not and those are the forces that were rallied in this conflict. --Cold Season (talk) 00:10, 2 August 2015 (UTC)[reply]
Okay, let's see what the sources you use actually say. In the Cambridge History of China, vol 7, page 226, it says "The first Mongolian campaign was launched in retaliation for the execution of a Chinese envoy sent to the Eastern Mongol khan Bunyashiri in 1409 and for the subsequent defeat of a large-scale punitive expedition led by General Ch'iu Fu". Bunyashiri, named as Öljei Temür Khan in WP, is listed as "the Mongol khan of the Post-Imperial Mongolia." Clearly, "Eastern Mongol khan" in your source refers to the khan of the Post-Imperial Mongolia, so the occurrence of "Eastern Mongols" here actually refers to the Post-Imperial Mongolia (as a contrast to the "Western Mongols" or Oirats). There should be a link to the article Post-Imperial Mongolia anyway. --Cartakes (talk) 00:29, 2 August 2015 (UTC)[reply]