The ambiguity of the Ryukyu kingdom's status is an interesting case to tackle because it does really take some getting into the diplomatic landscape (er, seascape?) of the region and period to properly contextualise. We need to set aside Westphalian ideas of exclusive sovereignty and approach post-1609 Ryukyuan statehood in terms of a negotiation between a variety of overlapping interests, which were in conflict in some cases but in concert in some others. What emerges out of that is an understanding that the narrative of continued Ryukyuan independence was not necessarily just a clever coverup: on the one hand, we can see it as a sort of mutually agreed fiction for mutual benefit; on the other, we can also see it as genuinely reflecting an ambiguous status on Ryukyu's part, where it really wasn't a clear-cut case of domination by 'Japan', however defined.

Firstly we need to give a little background on both the Chinese and Japanese sides of things. In Fairbank's old 'Chinese World Order' model, 'China', however understood, served as a fount of political legitimacy for the states of East Asia. Tributary states engaged in ritual gift exchange and in a rhetoric of subordination in order to obtain legitimation through recognition by the Chinese emperor. What has emerged since among historians is a counter-argument that the reverse was usually equally, if not more true: Asian regional powers could do without recognition by a Chinese empire, whereas Chinese empires derived considerable legitimation of their own from being acknowledged as being at the nominal centre of the East Asian political order. To use a Ming-Qing example, recent work by Yuanchong Wang has argued that recognition by Joseon Korea was integral to the Qing Empire's self-perception, as it both signified that the Qing had successfully assumed the Ming Empire's place in the East Asian order, and also, on a deeper level, served as an exemplar of a superior-subordinate relationship in the Confucian hierarchical worldview, certifying the 'Chineseness' of the Qing state within the broader Sinosphere. The Ryukyus can be seen in similar terms: it was important to the Qing that the kingdom was both independent and recognised the Qing state as legitimate, or at least that it appeared so. Of course, the tribute trade also had economic value, through which could be exercised a degree of hard power leverage, but we ought not to take a reductionist approach of presuming that all commerce was conducted through formal tribute arrangements as opposed to private enterprise.

On the Japanese side, we ought to bear in mind that Japan was not a unified state at this time, and indeed would not be until the latter half of the nineteenth century. Satsuma's status as a 'vassal' of the Tokugawa bakufu based at Edo ought to be understood as being one that was not a clear-cut position of subordination. Indeed, many of what the bakufu termed han ('domains') saw themselves as kuni ('countries'), independent states which conceded to a degree of Tokugawa interference. Satsuma formed an extra-special exception within the system, as, unlike basically all the other domains, it had the right to possess more than one castle, and so it maintained its own system of sub-fiefdoms. This autonomy was part of how it ended up able to sustain direct overlordship over the Ryukyu kingdom, such that it exercised its own layer of authority even as it fell within the broader jurisdiction of the Tokugawa bakufu. This did not mean, however, that Tokugawa rule was exercised exclusively through Satsuma: because the kingdom was a Satsuma vassal, it was also a Tokugawa vassal by extension, and the bakufu was able to exercise its own authority over it.

With that now discussed, let's look at the aftermath of 1609: under the terms of the 1611 surrender agreement whereby the Ryukyu kingdom submitted to Satsuma suzerainty, Satsuma received regular tribute, gained veto power over Ryukyu's trade policy, and it also required the kingdom to move towards appointing offices by merit rather than heredity. However, while the bakufu permitted Satsuma to receive tribute from the Ryukyu kingdom, it had also maintained that the Shō family of Chūzan would continue to occupy the throne. As a result, although Satsuma suzerainty eventually led to the erosion of the local nobility and Buddhist temples in favour of a new class of Confucian literati, it never managed to dethrone the royal house and establish the region as a direct province of Satsuma's mini-empire. Officially, the Ryukyus' agricultural output began to be listed as part of Satsuma's land value assessment starting in 1634, but this didn't inherently clear things up. You could, I think, make the argument that part of why Ryukyuan subjugation was never formally declared to the Ming or Qing was that there was a genuine ambiguity as to the relationship was between the kingdom, Satsuma, and the bakufu: was the Ryukyu Kingdom primarily a Tokugawa vassal, over whom Satsuma was granted administrative authority and entitlement to its revenues? Or was it fundamentally a Satsuma dominion, but one where the bakufu drew some red lines so that Satsuma didn't overstep its authority more broadly? Maintaining this Schrödinger's Cat state arguably suited all parties, as it allowed the royal line to stay in place, while neither Satsuma nor the bakufu had to risk conceding their part in the power-sharing arrangement depending on how the situation resolved.

Ryukyu would soon be confirmed in a considerable degree of autonomy even within its nominal subordination to its Japanese overlords. A 1624 memorandum from Satsuma stipulated, among other things, that 'people from other kuni' were forbidden from visiting the kingdom, which did not necessarily exclude those living in the Tokugawa's personal fiefdoms, but which did make Satsuma the only vassal han allowed to send its subjects to Ryukyu. While this would affirm that Satsuma was the only domain allowed to exercise authority over the kingdom, the extent of that authority was also more formally delineated: Satsuma renounced any ability to interfere in cases of capital punishment or exile, and in the long run there was the implicit understanding that Ryukyuans who were convicted of crimes in any Satsuma-claimed territory would be tried in Ryukyuan courts, in a massive concession to Ryukyuan judicial autonomy.

As argued by Gregory Smits, this round of concessions in 1624 was the result of Satsuma feeling the need to preserve an image of Ryukyuan independence in order to siphon off its continued tribute trade with the Ming. Ryukyu had sent tribute missions to the Ming court once every two years since 1522, but this had been reduced to effectively once every ten years during the period of 1612-22, and the reason was pretty simple: the Ming were not unaware that there had been an invasion, and were attempting to use the cession of tribute as a form of economic leverage to weaken Satsuma control. By restoring measures of Ryukyuan sovereignty, Satsuma hoped that the Ming would again allow a more regular exchange, and this ultimately paid off – the Ming allowed one mission every five years from 1622, and after the 1632 mission the Ryukyu kingdom was again permitted to trade biennially.

What ensued was what Okinawan historian Mamoru Akamine terms the 'policy of concealment': a mutual concession between the Ryukyu Kingdom, the Ming/Qing, Satsuma, and the Tokugawa bakufu that allowed all parties to achieve some form of acceptable outcome, despite a common implicit recognition of Satsuma suzerainty over the islands. The Ryukyuan royal house maintained its status and judicial authority, the Ming/Qing were able to continue to cite the Ryukyus as an independent state that accepted their supremacy, Satsuma was able to maintain what authority it could over the islands as well as siphon off Ryukyuan tribute, and the bakufu avoided conflict with China. An extra bonus was that every formal Ryukyuan visit to Edo was followed up by promotions for the Shimazu daimyo of Satsuma, which created an incentive within the bakufu-han relationship for Satsuma to maintain its suzerainty over Ryukyu without antagonising its continental neigbour.

The full mechanisms of the 'policy of concealment' came to be hashed out after 1667, four years after the kingdom stopped recognising the Ming (whose last loyalist remnants formed a rump state on Taiwan) and began paying tribute to the Qing exclusively in 1663, although it appears that they had been sending missions to both as early as 1655 with bakufu sanction. Officially, the Ryukyuan kingdom was independent, but told the Qing that they had a commercial arrangement with Satsuma domain on the island of Takarajima, in the same way that Tsushima (a domain ruled by the Sō clan) served as an intermediary between Japan and the Joseon kingdom, or how Dejima served as the intermediary for trade with the Dutch outside Nagasaki. Interestingly, it was Ryukyu's royal court which promulgated many of the regulations whereby the 'policy of concealment' was to be maintained: if a ship was wrecked off the Chinese coast, all Japanese-language documents were to be burned before the crew were rescued, as that would ensure their recognition as Ryukyuans and entitle them to shelter in Fuzhou, and from thence to repatriation. If Ryukyuan crew were part of a Satsuma ship that was wrecked, they would masquerade as Japanese in order to be sent back with the Satsuma crew. If Chinese envoys were present in Ryukyu to present investiture patents, any notion that the islands had a Japanese connection was to be suppressed: Japanese names, language, poetry, calendar, coinage, religious iconography, even Japanese-style tools were to be hidden away for the duration. The envoys were not allowed to leave the city limits of Naha, while Satsuma officials were temporarily relocated to a village outside the city.