(implausibly close?)
We have particle accelerators that achieve Lorentz factors of 7,500. I proposed a Lorentz factor of 22. Never mind a superintelligence, we, are on the brink of being able to accelerate nanomachines to that speed (assuming we had nanomachines).
The only implausible thing is being able to decelerate non-destructively at the target, and none of us have given that even 5 whole minutes of serious thought, never mind a couple trillion superintelligent FLOPS.
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I think the nearest deadline is our own lifespans. FAI is no good if you're dead before it comes along. Also cryonics requires fast economic growth.