So... is Shinsekai yori finished or not?
It is a bit ambiguous in this case.
Why?
The anime finished before the manga:
Anime finished: March 23, 2013
Manga finished: June 09, 2014
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
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
In a distant future where a portion of humanity possesses psychokinetic powers called Cantus, young Saki Watanabe finally awakens her abilities and joins a special academy.
Her seemingly idyllic life in the town of Kamisu 66 is quickly disrupted by disappearances and strange encounters with intelligent creatures called Monster Rats, who revere those with Cantus.
Saki and her friends, Maria, Shun, Satoru, and Mamoru, begin to investigate the mysteries surrounding their society, uncovering uncomfortable truths about the past and questioning the true nature of their seemingly utopian world.
Their quest for answers leads them down a path of self-discovery and challenges their understanding of the established order, suggesting a hidden darkness lurking beneath the surface of their perfect society.