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In episode 6, it was shown that Claudia Enfield is the 2nd rank. However, Julis-Alexia von Riessfeld said that Claudia is undefeated.

So, how can Toudou Kirin be ranked 1 if she never defeated Claudia?

  • It may due to Kirin got more victories than Claudia because Claudia is a president and no one dare to duel her. – ahaz joy Mar 18 '17 at 15:29
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I just watched this series a few days ago, Kirin is rank 1 because of overall combat ability being ranked higher due to 2 things:

  1. Kirin is not a strega
  2. Kirin does not use a lux in battle (at least before she fought Ayato)

Because of that, even though Claudia is undefeated, in terms of strength Kirin is viewed as stronger.

This gets discussed in a later episode of season 1, though I'm not sure which one exactly.

Edit

Just to clarify, Kirin does end up getting a lux later in the novel but it isn't shown in either of the anime seasons. She uses a normal katana

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