?? is it just some middle perversity for which poincare duality and so forth survive to the non-singular case ?? .... ?? "complementary perversities" here maybe ???? ..... ??? upper and lower middle as complementary ??? ....

?? hmmm, "Intersection homology groups of complementary dimension and complementary perversity are dually paired." (wpa) ..... ???? .....

?? "The (lower) middle perversity m is defined by m(k) = integer part of (k − 2)/2. Its complement is the upper middle perversity, with values the integer part of (k − 1)/2. If the perversity is not specified, then one usually means the lower middle perversity. If a space can be stratified with all strata of even dimension (for example, any complex variety) then the intersection homology groups are independent of the values of the perversity on odd integers, so the upper and lower middle perversities are equivalent." ... ??? don't remember how close i came to thinking it outloud, but i was vaguely imagining something like that happening ...

?? hmm, at the moment not seeing any perversity-dependence in wpa definition of "perverse sheaf" .... ??? .... ?? or stratification-dependence, even .... ??? ....

?? only one google hit for "middle perverse sheaf", none for "lower middle perverse sheaf" ... ?? ....

?? maybe that wpa is being sloppy ... ??? stratification as not pre-specified ... ??? while maybe mentioned core status requires pre-specification ?? .... ... ???? .....