Oh, is the Booster before the Core? It's been a while, I guess I got mixed up there, plus I haven't gotten the Booster 0.8 for probably the past five playthroughs.
And as for that tough jump when bypassing the Booster, there's a small marking on the platform you start on which is a perfect marking for where you need to jump to make it across.
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[NO BARKLEY NO PEACE]
If you can't slam with the best, then jam with the rest.