Question: When did the conquest of the Tang's biggest rival reach its peak?

full_context: Document 1: Sino-Tibetan relations during the Ming dynasty: The Ming initiated sporadic armed intervention in Tibet during the 14th century, but did not garrison permanent troops there. At times the Tibetans also used armed resistance against Ming forays. The Wanli Emperor (r. 1572–1620) made attempts to reestablish Sino-Tibetan relations after the Mongol-Tibetan alliance initiated in 1578, which affected the foreign policy of the subsequent Qing dynasty (1644–1912) of China in their support for the Dalai Lama of the Gelug school. By the late 16th century, the Mongols were successful armed protectors of the Gelug Dalai Lama, after increasing their presence in the Amdo region. This culminated in Güshi Khan's (1582–1655) conquest of Tibet from 1637–1642 and the establishment of the Ganden Phodrang regime by the 5th Dalai Lama with his help.
Document 2: Sino-Tibetan relations during the Ming dynasty: Laird writes that the Ming appointed titles to eastern Tibetan princes, and that "these alliances with eastern Tibetan principalities are the evidence China now produces for its assertion that the Ming ruled Tibet," despite the fact that the Ming did not send an army to replace the Mongols after they left Tibet. Yiu Yung-chin states that the furthest western extent of the Ming dynasty's territory was Gansu, Sichuan, and Yunnan while "the Ming did not possess Tibet."
Document 3: Sino-Tibetan relations during the Ming dynasty: Laird writes that Altan Khan abolished the native Mongol practices of shamanism and blood sacrifice, while the Mongol princes and subjects were coerced by Altan to convert to Gelug Buddhism—or face execution if they persisted in their shamanistic ways. Committed to their religious leader, Mongol princes began requesting the Dalai Lama to bestow titles on them, which demonstrated "the unique fusion of religious and political power" wielded by the Dalai Lama, as Laird writes. Kolmaš states that the spiritual and secular Mongol-Tibetan alliance of the 13th century was renewed by this alliance constructed by Altan Khan and Sönam Gyatso. Van Praag writes that this restored the original Mongol patronage of a Tibetan lama and "to this day, Mongolians are among the most devout followers of the Gelugpa and the Dalai Lama." Angela F. Howard writes that this unique relationship not only provided the Dalai Lama and Panchen Lama with religious and political authority in Tibet, but that Altan Khan gained "enormous power among the entire Mongol population."
Document 4: Sino-Tibetan relations during the Ming dynasty: While the Ming dynasty traded horses with Tibet, it upheld a policy of outlawing border markets in the north, which Laird sees as an effort to punish the Mongols for their raids and to "drive them from the frontiers of China." However, after Altan Khan (1507–1582)—leader of the Tümed Mongols who overthrew the Oirat Mongol confederation's hegemony over the steppes—made peace with the Ming dynasty in 1571, he persuaded the Ming to reopen their border markets in 1573. This provided the Chinese with a new supply of horses that the Mongols had in excess; it was also a relief to the Ming, since they were unable to stop the Mongols from periodic raiding. Laird says that despite the fact that later Mongols believed Altan forced the Ming to view him as an equal, Chinese historians argue that he was simply a loyal Chinese citizen. By 1578, Altan Khan formed a formidable Mongol-Tibetan alliance with the Gelug that the Ming viewed from afar without intervention.
Document 5: Tibet: The Tibetan Empire emerged in the 7th century, but with the fall of the empire the region soon divided into a variety of territories. The bulk of western and central Tibet (Ü-Tsang) was often at least nominally unified under a series of Tibetan governments in Lhasa, Shigatse, or nearby locations; these governments were at various times under Mongol and Chinese overlordship. The eastern regions of Kham and Amdo often maintained a more decentralized indigenous political structure, being divided among a number of small principalities and tribal groups, while also often falling more directly under Chinese rule after the Battle of Chamdo; most of this area was eventually incorporated into the Chinese provinces of Sichuan and Qinghai. The current borders of Tibet were generally established in the 18th century.
Document 6: Tibet: In 821/822 CE Tibet and China signed a peace treaty. A bilingual account of this treaty, including details of the borders between the two countries, is inscribed on a stone pillar which stands outside the Jokhang temple in Lhasa. Tibet continued as a Central Asian empire until the mid-9th century, when a civil war over succession led to the collapse of imperial Tibet. The period that followed is known traditionally as the Era of Fragmentation, when political control over Tibet became divided between regional warlords and tribes with no dominant centralized authority.
Document 7: Sino-Tibetan relations during the Ming dynasty: Patricia Ebrey writes that Tibet, like Joseon Korea and other neighboring states to the Ming, settled for its tributary status while there were no troops or governors of Ming China stationed in its territory. Laird writes that "after the Mongol troops left Tibet, no Ming troops replaced them." Wang and Nyima state that, despite the fact that the Ming refrained from sending troops to subdue Tibet and refrained from garrisoning Ming troops there, these measures were unnecessary so long as the Ming court upheld close ties with Tibetan vassals and their forces. However, there were instances in the 14th century when the Hongwu Emperor did use military force to quell unrest in Tibet. John D. Langlois writes that there was unrest in Tibet and western Sichuan, which the Marquis Mu Ying (沐英) was commissioned to quell in November 1378 after he established a Taozhou garrison in Gansu. Langlois notes that by October 1379, Mu Ying had allegedly captured 30,000 Tibetan prisoners and 200,000 domesticated animals. Yet invasion went both ways; the Ming general Qu Neng, under the command of Lan Yu, was ordered to repel a Tibetan assault into Sichuan in 1390.
Document 8: Sino-Tibetan relations during the Ming dynasty: Discussions of strategy in the mid Ming dynasty focused primarily on recovery of the Ordos region, which the Mongols used as a rallying base to stage raids into Ming China. Norbu states that the Ming dynasty, preoccupied with the Mongol threat to the north, could not spare additional armed forces to enforce or back up their claim of sovereignty over Tibet; instead, they relied on "Confucian instruments of tribute relations" of heaping unlimited number of titles and gifts on Tibetan lamas through acts of diplomacy. Sperling states that the delicate relationship between the Ming and Tibet was "the last time a united China had to deal with an independent Tibet," that there was a potential for armed conflict at their borders, and that the ultimate goal of Ming foreign policy with Tibet was not subjugation but "avoidance of any kind of Tibetan threat." P. Christiaan Klieger argues that the Ming court's patronage of high Tibetan lamas "was designed to help stabilize border regions and protect trade routes."
Document 9: Sino-Tibetan relations during the Ming dynasty: With the example of the Ming court's relationship with the fifth Karmapa and other Tibetan leaders, Norbu states that Chinese Communist historians have failed to realize the significance of the religious aspect of the Ming-Tibetan relationship. He writes that the meetings of lamas with the Emperor of China were exchanges of tribute between "the patron and the priest" and were not merely instances of a political subordinate paying tribute to a superior. He also notes that the items of tribute were Buddhist artifacts which symbolized "the religious nature of the relationship." Josef Kolmaš writes that the Ming dynasty did not exercise any direct political control over Tibet, content with their tribute relations that were "almost entirely of a religious character." Patricia Ann Berger writes that the Yongle Emperor's courting and granting of titles to lamas was his attempt to "resurrect the relationship between China and Tibet established earlier by the Yuan dynastic founder Khubilai Khan and his guru Phagpa." She also writes that the later Qing emperors and their Mongol associates viewed the Yongle Emperor's relationship with Tibet as "part of a chain of reincarnation that saw this Han Chinese emperor as yet another emanation of Manjusri."
Document 10: Sino-Tibetan relations during the Ming dynasty: During the Five Dynasties and Ten Kingdoms period of China (907–960), while the fractured political realm of China saw no threat in a Tibet which was in just as much political disarray, there was little in the way of Sino-Tibetan relations. Few documents involving Sino-Tibetan contacts survive from the Song dynasty (960–1279). The Song were far more concerned with countering northern enemy states of the Khitan-ruled Liao dynasty (907–1125) and Jurchen-ruled Jin dynasty (1115–1234).
Document 11: Sino-Tibetan relations during the Ming dynasty: Meanwhile, the Tumed Mongols began moving into the Kokonor region (modern Qinghai), raiding the Ming Chinese frontier and even as far as the suburbs of Beijing under Altan Khan (1507–1582). Klieger writes that Altan Khan's presence in the west effectively reduced Ming influence and contact with Tibet. After Altan Khan made peace with the Ming dynasty in 1571, he invited the third hierarch of the Gelug—Sönam Gyatso (1543–1588)—to meet him in Amdo (modern Qinghai) in 1578, where he accidentally bestowed him and his two predecessors with the title of Dalai Lama—"Ocean Teacher". The full title was "Dalai Lama Vajradhara", "Vajradhara" meaning "Holder of the Thunderbolt" in Sanskrit. Victoria Huckenpahler notes that Vajradhara is considered by Buddhists to be the primordial Buddha of limitless and all-pervasive beneficial qualities, a being that "represents the ultimate aspect of enlightenment." Goldstein writes that Sönam Gyatso also enhanced Altan Khan's standing by granting him the title "king of religion, majestic purity". Rawski writes that the Dalai Lama officially recognized Altan Khan as the "Protector of the Faith".
Document 12: Sino-Tibetan relations during the Ming dynasty: Wang and Nyima argue that the Ming emperor sent edicts to Tibet twice in the second year of the Ming dynasty, and demonstrated that he viewed Tibet as a significant region to pacify by urging various Tibetan tribes to submit to the authority of the Ming court. They note that at the same time, the Mongol Prince Punala, who had inherited his position as ruler of areas of Tibet, went to Nanjing in 1371 to pay tribute and show his allegiance to the Ming court, bringing with him the seal of authority issued by the Yuan court. They also state that since successors of lamas granted the title of "prince" had to travel to the Ming court to renew this title, and since lamas called themselves princes, the Ming court therefore had "full sovereignty over Tibet." They state that the Ming dynasty, by issuing imperial edicts to invite ex-Yuan officials to the court for official positions in the early years of its founding, won submission from ex-Yuan religious and administrative leaders in the Tibetan areas, and thereby incorporated Tibetan areas into the rule of the Ming court. Thus, they conclude, the Ming court won the power to rule Tibetan areas formerly under the rule of the Yuan dynasty.
Document 13: Sino-Tibetan relations during the Ming dynasty: Kolmaš writes that, as the Mongol presence in Tibet increased, culminating in the conquest of Tibet by a Mongol leader in 1642, the Ming emperors "viewed with apparent unconcern these developments in Tibet." He adds that the Ming court's lack of concern for Tibet was one of the reasons why the Mongols pounced on the chance to reclaim their old vassal of Tibet and "fill once more the political vacuum in that country." On the mass Mongol conversion to Tibetan Buddhism under Altan Khan, Laird writes that "the Chinese watched these developments with interest, though few Chinese ever became devout Tibetan Buddhists."
Document 14: Sino-Tibetan relations during the Ming dynasty: Tibet was once a strong power contemporaneous with Tang China (618–907). Until the Tibetan Empire's collapse in the 9th century, it was the Tang's major rival in dominating Inner Asia. The Yarlung rulers of Tibet also signed various peace treaties with the Tang, culminating in a treaty in 821 that fixed the borders between Tibet and China.
Document 15: Sino-Tibetan relations during the Ming dynasty: Nevertheless, the ethno-geographic caste hierarchy favoring the Mongols and other ethnicities were accorded higher status than the Han Chinese majority. Although Han Chinese who were recruited as advisers were often actually more influential than high officials, their status was not as well defined. Kublai also abolished the imperial examinations of China's civil service legacy, which was not reinstated until Ayurbarwada Buyantu Khan's reign (1311–1320). Rossabi writes that Kublai recognized that in order to rule China, "he had to employ Chinese advisors and officials, yet he could not rely totally on Chinese advisers because he had to maintain a delicate balancing act between ruling the sedentary civilization of China and preserving the cultural identity and values of the Mongols." And "in governing China, he was concerned with the interests of his Chinese subjects, but also with exploiting the resources of the empire for his own aggrandizement. His motivations and objectives alternated from one to the other throughout his reign," according to Rossabi. Van Praag writes in The Status of Tibet that the Tibetans and Mongols, on the other hand, upheld a dual system of rule and an interdependent relationship that legitimated the succession of Mongol khans as universal Buddhist rulers, or chakravartin. Van Praag writes that "Tibet remained a unique part of the Empire and was never fully integrated into it," citing examples such as a licensed border market that existed between China and Tibet during the Yuan.
ground_truth: 1642
sub_queries: Who was the Tangs biggest rival? Answer: Tibet
When did the conquest of Tibet reach its peak? Answer: 1642