Here's my update. Its overly detailed, but almost all of this stuff happened, I just changed it around a little.
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The first Roman Emperor of the 6th century was Anastasius, who reigned from AD 491 to 518. He was a devout Monophysite, which put him often at odds with the Orthodox establishment in Constantinople. He tried to install Monophysite Patriarchs, but faced riots. As a compromise to avoid further unrest, he had several laws passed to protect religious freedom for both Orthodox and Monophysite Christians. Other sects, such as Arianism, and other religions were not protected, however.
The Empire would find itself at war with Persia in AD 502, and suffered several setbacks early in the war. However, they were able to turn the tide of the war and made peace with Persia in 506. Anastasius then focused on building up the eastern defenses, especially at Daras.
Anastasius recognized Theodoric as king of Italy in AD 497, and worked to keep relations with the Ostrogoths peaceful throughout his reign. This cost the Romans some territory in Pannonia, but allowed them to bolster their Danube defenses against Bulgar raids. An expedition against the Bulgars was launched in 510, and was moderately successful, although the commander of the expedition, Vitalian, was killed in the fighting.
Anatasius also reformed the coinage system and taxation system. The tax system became more efficient and many taxes were actually lowered. At his death, Anastasius left a surplus of 220,00 lbs. of gold (100,00 less than in OTL, due to increased spending on border defenses).
Anastasius would be succeeded by Justin, commander of the excubitors, the elite palace guard. Justin reigned from AD 518 to 527. He broke with Anastasius' pro-Monophysite policies, though he did not repeal any of their legal protections. He did, however, support the Orthodox efforts to persecute them through religious channels. Still, these were almost totally ineffectual in Monophysite majority areas, and there were few problems, though Justin did have to reign in some of the more zealous members of the Orthodoxy.
All of this put Pope Hormisdas in a bind, as, on the one hand, he wanted to heal the wounds between the Orthodoxy of the East and West, and, on the other hand, he had to accommodate the Arians in the West. He tried to bring the Monophysites back into the fold, but had to abandon this effort when several clergy members criticized him for "attacking heretics that he would never face, while bowing before others". The end result of all this is that the Monophysites were free from persecution for the time being. Theodoric, meanwhile, kept relations with the Ostrogoths on good terms, partially by allowing the Arians in the Empire some degree of liberty, mainly because the Popes had to as well.
Things were not as smooth with Persia. Tzath, the King of Lazica (Colchis), a land regarded as a satellite of Persia, had gone to Constantinople to be baptized and crowned king in AD 522. This incensed Kavadh, king of Persia, who negotiated an alliance with Zilbigi, the king of the Sabiric Huns in the Caucasus, to attack the Romans. However, Zilbigi negotiated an alliance with the Romans as well. Justin let this leak to Kavadh. When confronted, Zilbigi confessed, and narrowly escaped the Persians with his life. Nearly half of the 20,000 Huns with him were not so lucky.
Justin managed to patch things together with Zilbigi, avoiding a potential conflict there. However, Kavadh now had a newfound sense of respect for Justin, and asked Justin to adopt his third son, Khusro, so that he could be the legitimate heir to the Persian throne (the eldest son favored a rebelious religious sect, and the second had lost an eye, making him ineligible). Justine refused to adopt him according to Roman law, as Khusro would then have a claim to the imperial throne, and offered to adopt him according to barbaric custom. This was unacceptable.
Kavadh then moved against the kingdom of Iberia, in the Caucasus. Justin decided to defend the Christian state, and sent Probus, nephew of Anastasius, to secure the aid of the Bosporan Huns for the Iberians. In the meantime, Zilbigi's Sabiric Huns went to aid the Iberians. The Persians were slowed by Zilbigi, long enough for Probus to come down with a force of Bosporan Huns. The Persians were now bogged down in Iberia.
Justin eventually launched raids into Persarmenia (the Persian controlled area of Armenia), under Sittas and Belisarius. The Persians were forced to abandon Iberia and face them. Sittas and Belisarius were prevented from making any progress, but they tied down the Persian army in Persarmenia. This allowed Probus and Zilbigi to attack Caucasian Albania, on the Caspian Sea.
Eventually, peace would be reached, with Lazica, Iberia, and Albania confirmed as client of the Romans, while Persarmenia lost a sliver of northern territory.
Justin would be succeeded by Justinian, his nephew and adopted son, who also was a major power behind Justin's administration. Justinian would rule from AD 527 to AD 565. He and his wife, Theodora, would be some of the greatest rulers of the Empire.
Justinian would vigorously persecute the Manichaeans, pagans, and Samaritans. Jews were treated fairly well, as were the Monophysites (Theodora herself was a Monophysite). Arians would not fair as well after Harbidus succeeded Theodoric in the west, as Harbidus was Orthodox himself, thus negating the political reasons for tolerating Arianism. The only major unrest Justinian faced was the infamous Nike Revolt, but his reaction to the revolt left Justinian firmly in control and gave him the opportunity to restore the Hagia Sophia to its present glory.
The Romans and Persians would go to war in 529, when the Persians attacked the Roman fortress of Daras, which was built in violation of treaty obligations. Belisarius defeated the Persians at Daras and defeated them again at Callinicum. Sittas meanwhile invaded Persarmenia. When Kavadh died and was succeeded by Khusro, the Persians began to seek peace, so Khusro could consolidate his position. However, the Romans were wining, and Justinian wanted, at the very least, Armenia. The Romans continued to win victories until 536, when Khusro accepted Roman control of all of Armenia. The Persians and Romans would go to war again in the 540s, though Justinian negotiated a peace by paying a moderate indemnity.
The rest of Justinians' reign would be fairly peaceful and uneventful, except for the coming of the Bubonic Plague in AD 542. Justinian also reformed the legal structure of the Empire with the Codex Justinianus.
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