In this talk we will see how to construct an explicit unbounded representative of the defining extension for a Cuntz-Pimsner algebra (associated with a finitely generated bi-Hilbert module). An analogue of the "lag" appearing in the shift tail equivalence appearing in one-sided subshifts of finite type defines an unbounded operator that assembles to an unbounded Kasparov module. The a more general setting the "lag" measures a type of depth below the core in the Cuntz-Pimsner algebra. This is joint work with Bram Mesland and Adam Rennie.