  Recent work on optimization problems in random link models has verified
several conjectures originating in statistical physics and the replica and
cavity methods. In particular the numerical value 2.0415 for the limit length
of a traveling salesman tour in a complete graph with uniform $[0,1]$ edge
lengths has been established.
  In this paper we show that the crucial integral equation obtained with the
cavity method has a unique solution, and that the limit ground state energy
obtained from this solution agrees with the rigorously derived value. Moreover,
the method by which we establish uniqueness of the solution turns out to yield
a new completely rigorous derivation of the limit.
