Most TVs have 4-digit serials, which are procedurally-generated. Serials below 4 digits are manually assigned.
These would be rendered verbally as 'triple-zero-one' and 'triple-zero-two'. These two units very rarely need to reference their serials because of their status; everyone already knows who they are.
Serials 0003 to 0009 are currently unused.
Currently Polycephaly has the only 2-digit serial: 0010, rendered verbally as 'double-zero-ten'. Again, Polycephaly rarely has cause to refer to themself by serial. Being the only large unit in their faction makes them pretty distinctive.
Serials 0011 to 0099 are currently unused.
Currently not in use. Serials 0100 to 0999 are available and will likely be allocated for research/experimental purposes.
As used by standard TV-units.
While it is physically possible to build a TV shell, load a new software brain into it and power it on, this is not recommended and not done. A unit built in such a way would likely be forever a stimulus-response machine rather than developing full self-awareness or much of a personality, would likely have poor control over its screen powers, and would not necessarily even be loyal to its own faction.
Instead, units are 'born' as software in server farms called 'creches', where they start off as simple programs and gradually bootstrap themselves into self-awareness, moving onto simulated training until they're ready to be uploaded into actual hardware bodies. In this way, you end up with a unit with a proper theory of mind and personality, that's loyal to its faction.
(I am assuming the above is also true for Cameras and Speakers, but I haven't explored this in my fics. I think the TVs must take longer to create given that there are comparatively few of them, perhaps because they have all their screen and teleport powers to master before they can be allowed to let loose with a real body.)
The 4 digits are allocated as follows:
The creches and servers can have only numbers 1-9 (not 0), so there are 8,400 possible serials (rather than 9,999). (Technically slightly fewer still, since as author of my stories I will forbid the use of numbers associated with hate groups.)
Cygnus, for example, has the serial 5022 (rendered verbally as Fifty-Twenty-Two). This tells us they were generated in server 2 within creche 5, and were activated on a day ending in 2 (the 02nd, 12th or 22nd). The zero is just a random identifier to distinguish them from any other TVs that happened to be generated on the same day from the exact same server. (This has yet to happen in practice. It's rare for more than 1 TV to come into existence on the same day. Plus, most of the nascent softwares will simply error out of existence rather than become sentient.)
The Titan's chief engineer has the serial 1668 (Sixteen-Sixty-Eight), and the Titan themself had the serial 1791 (Seventeen-Ninety-One) when they were a normal pre-Titan unit. This tells us that both the Titan and its main engineer were generated in the same server farm (1), but on different servers.
(I've no idea what system the Cameras and Speakers use. I'm inclined to think the Cameras just have sequential serials because they're squares like that.)
The Imperator's (TV Matriarch's) two bodyguards have the serials 1153 and 1566, but they are a rare exception, as these aren't their original serials. There were 16 candidates for being remade into the Titan, and the two bodyguards were 2 such candidates. All the candidates had their serials expunged and new ones allocated, so that no-one (besides the chief engineer and the Titan themself) would know which candidate had become the Titan. The two bodyguards have hypothetical serials (as do the other 13 candidates that were considered for Titanhood).
Feel free to steal any parts of this you like for your own OCs/fics; I don't own the concept of allocating numbers.
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