The Han dynasty
In 145 BC, a war began that lasted several centuries. The Empire is the same as that of the OTL, even ending the same year for the same reasons, but easier as war exhaustion had a greater toll on China than the Confederation. The war was started by the Han, but the Bactrian Kallipolis had been considering moving their philosophy there for the past year. Overall, the war lasts for around 253 years, as neither side was willing to negotiate and resulted in stalemate. However, while the Confederation could absorb large losses, China was less able to. Several new technologies were developed by both nations during the war, such as pistol crossbows, telescopic pikes, automated steam powered artillery and portable Archimedean burning glasses. However, the Roman leader Trajan arrived through Hsiung-Nu territory, with several recruited as allies. This forces negotiations and allowed China the North, while the Confederation received the south. However by 220, the Empire falls apart fast due to growing rebellion and discontent.
The Sui dynasty
In 534, the Byzantine general Belisarius had arrived to conquer China, however China is able to defend against against this less diverse enemy. The war only lasted 4 years despite popular support, as only Constantinople was really interested, thereby lacking the earlier wars manpower and technical ingenuity.
The Yuan dynasty
Also known as the Mongol Empire due to the dominance of northern Mongolian tribes. In 1220, the Mongol leader Temujin, known forever as Genghis Khan as nicknamed by his Middle Eastern enemies engages in a brutal war against the Confederacy, reaching Hungary. However, Kallipolic agents were able to assassinate him and his son, rendering the horde leaderless. So far, this was the greatest Chinese attack on the Kallipolic Confederation.
Although they had been doing so for years, Chinese agents were also able to steal more Confederate technology, than ever (they already had metal ships and a form of air travel, with powered engines that don't just rely on oars or sails). The Imperial family were also encouraging domestic innovation in civil science, such as clocks farming methods and architecture. Around the same time, a fleet from China, built from stolen blueprints for the Indian Hāthī class freighter (which are similar to the modern OTL Indian Godavari class frigates, though are slower and inferior in nearly every way, but were still able to make on oceanic crossing), on its way to a voyage through the Pacific islands was blown off course by an intense storm and embarked on an oceanic voyage after its compasses and navigational equipment were destroyed. Reaching the coast of what we call California, the fleet claims the land in the name of the Middle Kingdom. A colony was set up a year later, known as New Shanghai. The dynasty also launched an invasion of Japan under Kublai Khan, but a kamikaze stopped that.
The Ming dynasty
Eventually the Mongols were driven from power and a new Chinese dynasty was set up. Much of its history is the same as that of the OTL, but with more advanced technology. By 1588, China and the Confederation were in a space race. While the Chinese reached space first, the British Kallipolis gets the astronauts Francis Drake, John Hawkins and Martin Frobisher to the Moon. Frobisher stayed in the Apollo pod while Hawkins and Drake landed. Drake was the first to step out. For several decades after, both Chinese and some Confederate citizens claimed the landing was a fake, but by 1605, the landing was allegedly independently verified by the independent Aztec-Mayan space program (who used equipment of Confederate manufacture and therefore were not considered a reliable source by the Chinese). The Empire experienced a surge of growth in this period, going through the north all over Russia and stopping just off the Polish Kallipolis. However they, the Norse and the Persian Kallipolli repelled further advances.This situation led to a new land of the Border Princes who fought off Chinese and Confederate control fiercely.
The Qinq dynasty
In the 1600s the Ming dynasty and China began to decay, while the tribes of Manchuria began to unite. Invited to restore order, they did... by taking over. Believing themselves superior to the Chinese, imposing many laws on them, they also adopted much of Chinese culture for themselves. In 1700, the European and Chinese colonies began their own private war, separate from their mother Kallipoli. Conflict erupts all over the Americas except for the Caribbean, which is only European and Native American. Most conflict takes place in Central America, where the rival sets of colonies are closest. Others occur in North and South America, but less in the South as the Amazon Rainforest restricts incursions from both sides. China actively intervenes on behalf of its colonies, while the Confederation stays outside, except for Spain, Morocco, France and Ghana. 6 wars are fought in total, with a permanent peace deal in 1776, returning the colonies to status quo ante bellum. The Tiangong space station was built during this period.
However, the Chinese Empires acts of intervention drained it of soldiers that could have been used elsewhere. The Confederation had started to introduce the drug opium to the Chinese, hoping to undermine the Confucian state through subterfuge rather than force. A war starts in 1842 and finally finishes off the Confucian Chinese Empire. Kallipoli involved include India, Afghanistan, Russia, Kazakhstan and perhaps the Magnesia Moonbase and its advanced orbital weapons installed that year if one considers it a separate state. China was forced to give Hong Kong and Macau up to direct Confederation control while the Platonic powers moved in and occupied the country. Forced conversion was introduced, all Confucian establishments abolished and government positions were occupied by Platonic Chinese. All Chinese territory including any space installations were seized.
Classical: Chang'an, Wu, Yu,Bingzhou, Jiaozhou, Jingzhou, Jizhou, Liangzhou, Qingzhou, Xuzhou, Yangzhou, Yanzhou, Yizhou, Yongzhou, Youzhou, Yuzhou, Pingzhou, Qinzhou, Liangzhou, Ningzhou, Guangzhou, Sizhou, Mongolia, South Vietnam, Burma, Korea.
Medieval: Khwarezm, Iran, Laos, Xinjiang, Ningxia, Steepe Nomads, Kazhakstan, Punjab, Turkmenistan, Khmer Empire, Ukraine, Hungary, Bulgaria, Serbia.
Age of Division: Jiāzhōu New Shanghai (California), Ālāsījiā zhōu (Alaska), Měiguó dōngbù (East American Territiories), Tartarstan, Yakut, Khakassia, Rus, Eastern Europe Territiory, Kenya.
The downfall of Confucianism: Chinese Colonial Vassals, Manchuria Exclusion Zone.
(Overall technology can be found here). Much technology was copied from the Platonics, but the Chinese were pioneers in Rockets. They also developed a steam powered drill in 220 BC, a way of transporting natural gas to homes in 200, repeating and multiple crossbows, landmines and in 400 BC a bamboo helicopter that never really saw widespread use. Overall sometimes they were more advanced and sometimes not. In terms of tech and culture, the Chinese Empire was almost a mirror image of the Confederation. In the space race the Chinese were actually better as shown above.
The Chinese economy was mostly self sufficient, with there being widespread trade throughout the vast empire. As a result of the hostility between it and the Confederation, outside trade was mainly with neutral countries unconquered by either side. Even during peace there were frequent trade embargoes between the two empires. Most inter empire trade was through smuggling.
Note that due to the "all under heaven" principle covered below trade with non-empires was not seen as trade but as the foreigners paying tribute and the Chinese giving them gifts.
The main ethical code is Confucianism. Like Platonism this is not a religion but could be seen as one. Kong-fu-zi however claimed that women should do as they're told, some claiming that he said the only virtuous woman was an uneducated one. It also showed disdain for international trade and suggested the Emperor was in charge only due to a Mandate of Heaven. All rulers are subordinate kings. This "all under heaven" principle was official but few believed it in practice. Much of this was the cause for the repeated Chinese-Confederation wars. In the latter half of the Empire, starting under the Yuan, women got an equal status to men in order to discourage any more deserters to Platonism. In former Platonic lands that China conquered, the women proved to be the most determined resistance movement because if they failed they feared they'd be reduce to subservient house servants. This was a bit of an exaggeration but the defections encouraged the Imperial government to make progress. This still didn't prevent the Confederation smuggling in opium and provoked another war, causing the fall. Not only was the Confederation more powerful at this point, but Chinese commanders and troops were disrupted by communications problems, with some even being addicted to opium- the drug they were trying to stop.
Until the Platonic conquest, Confucianism was the main ethical code of China and often doubled as a religion despite not having an established organisation or places of worship. Also popular is Taoism, which did survive the conquest. The Book of Lord Shang was already popular among Platonic Chinese and was made compulsory reading after the Platonic conquest on the grounds that it had women in warfare and that it was anti-Confucian (the Confederation was determined to eradicate its rival).
Shenism, the traditional folk religion is the largest actual religion, along with Buddhism. Zhuang Moism, Yi Bimoism, Tibetan Bön and Mongol shamanism are indigenous regional faiths. There is also a "Religion of the Pure and True" that exists in Ningxia province in northern China that holds a great similarity with the Arab based religion Islam. Missionaries from Europe have also attempted to introduce Christianity to China but with limited success. However the Russian Orthodox Church had a large amount of converts following the incorporation of Russian territory into the Empire.