HR 8799 is a nearby star hosting at least four \sim 10 \mbox { m } _ { { \mbox { \scriptsize Jup } } } planets in wide orbits up to \sim 70 au , detected through the direct , high-contrast infrared imaging .
Large companions and debris disks reported interior to \sim 10 au , and exterior to \sim 100 au indicate massive protoplanetary disc in the past .
The dynamical state of the HR 8799 system is not yet fully resolved , due to limited astrometric data covering tiny orbital arcs .
We construct a new , orbital model of the HR 8799 system , assuming rapid migration of the planets after their formation in wider orbits .
We found that the HR 8799 planets are likely involved in double Laplace resonance , 1e:2d:4c:8b MMR .
Quasi-circular planetary orbits are coplanar with the stellar equator and inclined by \sim 25 ^ { \circ } to the sky plane .
This best-fit orbital configuration matches astrometry , debris disk models , and mass estimates from cooling models .
The multiple MMR is stable for the age of the star \sim 160 Myr , for at least 1 Gyr unless significant perturbations to the N -body dynamics are present .
We predict four configurations with the fifth hypothetical innermost planet HR 8799f in \sim 9.7 au , or \sim 7.5 au orbit , extending the MMR chain to triple Laplace resonance 1f:2e:4d:8c:16b MMR or to the 1f:3e:6d:12c:24b MMR , respectively .
Our findings may establish strong boundary conditions for the system formation and its early history .