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Red or Blue?
The pun on the word senten is that it can translate to either a mantle (cape) or a bruise.
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Sato and Bones remark that their badge is iridescent which means it can look like many different colors. It mainly looks green in the series.
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Haruto's dad is likely a Catholic minister since Haruto prays at a statue of Maria-sama (St. Mary).
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Haruto can summon specific school spirits by holding out whatever combination of emblems he wants between his fingers. Haruto typically holds out up to six badges. The principal doesn't normally get summoned as he is usually on the scene but he gets his two seconds of appearance time at the end of the summoning sequence.
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Summoning order for the series
Haruto: Everybody assemble, on the double. Welcome!
Pink – Hanako
Yellow – Nino
Purple – Giant
Red – Red Mantle
Orange – Mirror Girl
Green (Iridescent) – Sato and Bones
Blue - Principal