  This paper addresses the existence of codimension one stable manifolds for
the pseudo-conformal blow-up solution for critical one-dimensional NLS. By the
work of Perelman and Merle, Raphael, the blow-up rate of these solutions is far
from the generic one. However, Bourgain,Wang and Perelman formulated the
possibility of codimension one stable manifolds for the non-generic blow-up
solutions. This paper established the existence of such manifolds, albeit only
in the measurable category.
