So this is how the story goes: in 2007 Chris Squire called up Rickenbacker and asked for six unfinished/unassembled 4003 husks to be painted by British painter Paul Karslake, who had painted Squire’s custom “Fish Out of Water” bass. At least three of those basses were painted by Karslake, with pastel “perimeter bursts”. That’s the story. Here’s what we can validate.
Those three basses exist. Here’s the “blue” one:

Karslake did paint them, although it took a couple years to get to it. All are signed inside the pickup cavity, and Karslake produced certificates of authenticity for them.

They were delivered from the factory unfinished and unassembled. We can validate that from in process photos of the “yellow” one without a clear coat or any holes drilled.

All were finished out with vintage appointments like a long pickguard, a toaster at the neck and a horseshoe at the bridge, as seen here on the “pink” one.

Oddly enough, all three feature a 4001C64 style “backwards” truss rod cover.

There is some question as to whether or not Squire ever took possession of the guitars, as no photographs have surfaced of him with them. As Squire died in 2015 and Karslake in 2020 we will likely never know.

I remember that “yellow burst” one was up FOREEEEEEVER on Reverb! I always wondered the full scoop on it!