Vanishing of beta function of non-commutative Φ44 theory to all orders

The simplest non-commutative renormalizable field theory, the ϕ4 model on four-dimensional Moyal space with harmonic potential is asymptotically safe up to three loops, as shown by H. Grosse and R. Wulkenhaar, M. Disertori and V. Rivasseau. We extend this result to all orders.