  We compute the exact, all energy scale, 4-point function of the large $N$
double-scaled SYK model, by using only combinatorial tools and relating the
correlation functions to sums over chord diagrams. We apply the result to
obtain corrections to the maximal Lyapunov exponent at low temperatures. We
present the rules for the non-perturbative diagrammatic description of
correlation functions of the entire model. The latter indicate that the model
can be solved by a reduction of a quantum deformation of SL$(2)$, that
generalizes the Schwarzian to the complete range of energies.
