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He is technically interacting with reason.
And as far I know reason itself is a concept type 1. Do I am not sure how it gonna correlate to that feat.
So how do you suggest it?
AE 1 interaction (concept type : (reason))
Or
AE 1 interaction, law manipulation
Him being irrelevant to reason was stated both in manga and databook probably.
It seems more related to law like Lille's at best who also operates under similar nature. The reason why he is called creature of "reason" specifically is due to the nature of him enforcing unbiased judgement on those who tries to deny the rule of moving on from there and punishing them via throwing them outside of time's flow.
Him ruling space-time is obvious because he is the one who had control over dangai, nothing really abstract about it.
Soo yeah, Lille type intangibility is suitable for the most part.