So... is Seireitsukai no Blade Dance finished or not?
It is a bit ambiguous in this case.
Why?
The anime finished before the manga:
Anime finished: September 29, 2014
Manga finished: March 25, 2019
We could not confirm the source content in MangaUpdates.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Kamito Kazehaya, a young man with a mysterious past, unexpectedly finds himself at Areishia Spirit Academy, an all-girls school dedicated to training elementalists, young women who contract with spirits.
His arrival is marked by an unusual encounter with Claire Rouge, leading to Kamito inadvertently bonding with a powerful spirit intended for her.
Now the only male student at the academy, Kamito is reluctantly drawn into their world, motivated by a desire to learn about his previous connection to a spirit named Restia Ashdoll and at the behest of the academy's headmaster.
He agrees to participate in the upcoming Blade Dance, a prestigious battle festival, despite the immense challenges and dangers it presents, including facing a powerful elementalist rumored to wield a dark spirit.
His time at the academy will be filled with difficulties and the need to adapt to his unique position amongst the shrine princesses-in-training.