  Based on large N Chern-Simons/topological string duality, in a series of
papers, J.M.F. Labastida, M. Marino, H. Ooguri and C. Vafa conjectured certain
remarkable new algebraic structure of link invariants and the existence of
infinite series of new integer invariants. In this paper, we provide a proof of
this conjecture. Moreover, we also show these new integer invariants vanish at
large genera.
