  We give a geometric interpretation of the coefficients of the HOMFLYPT
polynomial of any link in the three-sphere as counts of holomorphic curves. The
curves counted live in the resolved conifold where they have boundary on a
shifted copy of the link conormal, as predicted by Ooguri and Vafa.. To prove
this, we introduce a new method to define invariant counts of holomorphic
curves with Lagrangian boundary: we show geometrically that the wall crossing
associated to boundary bubbling is the framed skein relation. It then follows
that counting holomorphic curves by the class of their boundary in the skein of
the Lagrangian brane gives a deformation invariant curve count. This is a
mathematically rigorous incarnation of the fact that boundaries of open
topological strings create line defects in Chern-Simons theory, as described by
Witten.
  The technical key to skein invariance is a new compactness result: if the
Gromov limit of J-holomorphic immersions collapses a curve component, then its
image has a singularity worse than a node.
