Today, there are 101 papers on mathscinet using the notion of planar algebra, discovered by V. Jones in 1998.
As V.S. Sunder pointed out to me, the fundation of planar algebras theory is waiting for some detailed proved with all i's dotted and t's crossed, see for example the post:
What's the detailed proof of "the composition of planar tangles is well-defined"?
Sebastien Palcoux
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