Essential part (4)
(Other definitions for crux that I've seen before include "Most important aspect" , "Point of difficulty" , "Main point (of the matter)" , "Essential point of problem, decision etc" , "Most important point at issue" .)
'essential part' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for pith that I've seen before include "Tissue beneath citrus fruit rind" , "Spongy tissue like that lining an orange skin" , "nub of matter" , "Tissue inside the rind of citrus fruits" , "Lining of rind - important part" .)