Split/Second PSP has 2 main techs that allow faster times. The Elite GT12, the car I use here, is obligatory to use as it's the fastest by far on the PSP version.
Now to the 2 main speed techs.
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Explosion canceling. In Split/Second PSP, every explosion can make your car randomly start a drift if you're turning while you get hit. Drifting is really slow in this game as it makes your tires spin instead of keeping the grip. But if you hit a wall or slide along a wall after an explosion, the explosion slowdown effect gets canceled. So if you stay extremely close to a wall right before an explosion you get pushed into the wall by the explosion so the explosion effect gets canceled immediately, causing you to not lose any time. It often looks as if you would clip into the wall. On the 2nd to last corner on this track you can't avoid the explosion completely, but you can hit the opposite wall to cancel the effect sooner. The setup I use here works 99% of the time and it's really fast.
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Driftless drifting. In comparison to Split/Second on PC, X360 and PS3 drifting is generally way slower than just driving straight, especially with the Elite GT12. The GT12 is the fastest car in the game by far but really gets slowed down when you drift. So by tapping the brake mid-turn and letting go of the controls it's possible to take really sharp corners without hearing the tires screech - instead the car even accelerates again during that corner.
I believe there are a few more frames to be saved, but sub 1:02 seems impossible unless we find an OOB shortcut on this track. This is as optimized as it gets although the very last corner still has potential. This time is really tight.