(English Translation by Sidier): It normally works as a "masked patrol car". It's not made by the Space-Time Police, but Phoenix got it from somewhere else. Despite being its first time to run a race, it runs very smoothly. It's a hi-spec machine come from the future, and has functionalities that can allow it to win, but it's actually purposely using limiters to downgrade its performance.
Nintendo Power F-Zero GX Player's Guide
The Rainbow Phoenix is usually used as an undercover patrol car. It wasn't built by the Galactic Space Police, though--Phoenix designed and built it himself in secret. It's tuned to be a very easy machine for novice pilots to control. Since it's actually a machine from the future made with an unknown advanced technology, it has the ability to win the championship easily. Because of this unfair advantage, a limiter has been installed to reduce its capabilities. The Rainbow Phoenix currently runs at only 80 percent of its potential.
Notes: The designer of the machine is stated to be unknown in the F-Zero GX Complete Guide and the Nintendo Player F-Zero GX Player's Guide. As for why the bio states that Phoenix is the designer, is not known. Additionally, none of the other sources mention anything about running at 80 percent of its potential, only the fact that it has limiters. This could either be to prevent a time paradox, or because the machine itself is capable of time travel or some other ability the world is not currently ready for.
F-Zero GX in-game CARDT data
This machine normally serves as a police car besides the F-ZERO Grand Prix. Instead of taking the official Space Police Car, Phoenix found this machine for himself from somewhere. Though it's the first time to participate the grand prix, he has done quite a good tuning that makes it easy to drive.
Trivia[]
The RP in the machine's engine stat likely stands for Rainbow Phoenix.
