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Lyoko is the OS
Towers all have equal access to the processing power of the supercomputer.
Carthage is a virtual representation of the software core.
The Carthage Panel allows access to system software (Lyoko’s data, core programs, XANA, the kernel etc.)
The 36 Standard Towers allow access to application software (the modems, text files, media players, matt/dematt/devirt/virt programs etc.)
The 4 Way Towers act like servers for their sector, and also have a larger degree of virtual memory to support the large amounts of data they are handling.
The Super-Tower is the junction-box for all data streaming into and out of Carthage.
One of XANA’s designated roles is to guard Carthage – thus he has a greater degree of control there than in other sectors.
Carthage is hidden from view unless a person is told it exists – much like Aelita’s lost files which still exist but are undetectable. This is why Jeremie only discovered Carthage when the way was shown to him. Most likely the same applies to Aelita’s memory fragment in ‘The Key’.
Lyoko is run from Carthage, distributed through the way towers and executed through the nine Standard Towers to each sector.
Data mainly flows out from Carthage – a small amount is allowed to enter, but for large files to enter you need the Transporter (unless you deactivate the firewalls).
Towers distribute data to their sectors – all monsters come through Towers from Carthage (the data at least) – when the kids virtualise their data is entered into Lyoko through the towers etc.
The computer architecture only allows operation of the supercomputer through existing as a virtual being in Lyoko. The Console (we presume) can take control of all functions, but only if one has the correct codes (most likely genetic based or tied to the keys to Lyoko).
The Keys to Lyoko allow programmer access to all aspects of Lyoko and Carthage.
The console by default allows passive monitoring of the system core, and manipulation of application software, unless blocked by the Carthage Panel.
Tower interfaces only allow passive monitoring and use of certain programs for users – only Aelita can use the interfaces to actually modify and control all of the tower’s application software.
Feel free to add to this
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Here is a diagram I drew up to outline some of these elements.
If you can give me some feedback - point out errors, confirm, suggest alterations etc I think we can be done with this!

Cheers!
TB3