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Is it accurate to call the system headed by Taizong a federation? Moreover, which scholar asserts that it was or describes it as a federation. I say this because this user did not bother citing a source(s) which he used to write this passage. The Gokturks certainly pledged fealty to Taizong as their khagan, and Tibet was part of the Tang's tributary system (when they weren't battling with the Tang over Central Asia and access to the Silk Road). But a federation? I want to know how scholars classify the relationship between Tang China, Tibet, and the submitted Gokturks.
Whether the heavenly khaghan "empire" formed a federation is actually hotly debated in the Chinese and Japanese academic community. There are published books such as the Heavenly khaghan administrative system by Lin Tianwei 林天蔚的《天可汗制度》, Luo Xianglin's (Tang dynasty heavenly kaghan administration study),
罗香林《唐代天可汗制度考》and Yao Dazhong's "the functions of the heavenly kaghan international system" The most informative source for this study is the Tong Dian which recorded a speech made by Tang Taizong: "I am the Son of heaven of Tang, but below, I also carry out the duties of Kaghan. 我为大唐天子,又下行可汗事乎?" The common view
The Tang Lu Shu Yi seems to hint that the Tang code at least served as a crude "international law" for the different jimi prefectures. According to the volume 6, 异类相犯者,以法律论。"mutual hostility between different people(ethnic groups) will be settled by the (Tang) law accordingly. The heavenly kaghan therefore theoretically served both as a sort of "federation" where the Tang emperor was its head for the jimi fuzhou states, as well as an international court(a crude form of the UN) to maintain peace both within the Tang empire and without(including the tributary states like Koguryo and Tuyuhun which were Tang vassals but not under the jimi system). It was once thought that the heavenly kaghan had an administrative system itself, but the fact that this title applied to later Tang emperors like Xuan Zong and Su Zong as well shows that the Heavenly Kaghan might have originally been somewhat of an organization as well as an honorary title that eventually became only an honorary title. This title designate a ruler that was above all other kaghans and fit to rule all.(It is possible that later Uighur rulers adopted the title themselves). In any case, the Tang period appeared to be when a Chinese ruler's prestige reached its zenith. The only other period where a ruler reached such a high prestige in Chinese history was during the Yuan dynasty.
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Borjigin Ayurbawarda is probably the best member to ask about Tang-Tibetan relations, but I don't think Songtsan Gampo saw himself as Taizong's subject or vassal even after he married a Tang princess. Certainly Songtsan's successors did not see themselves to be under Tang authority, as clearly evidenced by the numerous wars between the Tang and Tibetan empires following Songtsan's reign.
Its doubtful that any non-confucian vassal states really saw China as its true sovereign, Tibet's situation might have been similar to those of Thailand and Burma's during the Qing dynasty, ritually, they were vassals and in their letter to the emperor, they addressed themselves as such, while the Tang ruler addressed himself as a superior, while the protocol maintained between them also designate a superior inferior status, but in their own court, they treat the Tang as just another state. But the fact that Gampo provided auxiliars to the Tang on 2 different occasions and even wrote to the Tang emperor that he can be counted on for trouble, as well as the Tibetan appeal for Tang aid in their struggle with the Tu yu hun. shows that the early Tang at least exerted some influence over the Tibetan state.