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So, for the sake of uniformity, do what names are we using for Nine/Arata and Twelve/Tōji? For the sake of convenience and recognition (since, so far, their school names were only used in episode 1), I prefer the numerical names.
Assuming that both are official names, I would stick with the names more frequently used in the work and keep the section in the description explaining the names.
Problem is, if we're going by how often the names are used, then by technicality we should be calling 'em Sphinx 1 and 2 >_<
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How well does it match the trope?