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Sophia (ソフィア, Sofia) is an antivirus software created by ALGOS using the retrieved data of Aura from the Akashic Records. Up until the events of Bullet, the Sohpia Squadron was controlled by Urania, an American based hacker under the orders of Veronica Bain (CEO of CyberConnect).
The dark Sophia in the OVA, based on information in the .hack movie, is likely a virus-infected anti-virus program which normally would have protected against the virus being unleased, but instead infected players and put them in comas.
The Sophia Squad was controlled by the hacker Urania in order to assist in the defeat of Drain. The entire batallion massacres the rats containing Deadly Flash in the battle at Net Slum.
.hack//Beyond the World
An updated version of Sophia appears in the .hack movie. It appears that they are actually anti-virus programs sold commercially by CC Corp. The World contains many Sophias which arrive in areas being attacked by viruses and glitches. They are controlled by a main Sophia called Auto Sophia who performs something akin to a Data Drain on viruses.
It is later revealed that CC Corp was able to replicate Data Drain, and created the Sophia programs with these abilities in order to be mass-produced as anti-virus software. Furthermore, the mutating Virus Bug was shown to have also been released undercover by CC Corp in order to promote this new product. However, the virus proved to evolve too fast for the Sophia programs to subdue, and it soon began to hunt them instead.
Kite(Sora) witnessed a group of Sophias be absorbed by the Virus Bug before it was Data Drained by the Auto Sophia. Unfortunately, the data of the engulfed Sophia programs was incorporated into the virus data during Data Drain's rewriting process, evolving it into an all-powerful virus which emerged from the Drain and devoured Auto Sophia.