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That’s the point of having a global central bank. They would manage it, and we would want to ensure that all appropriate mechanisms for oversight and accountability were in place. Transparency would also be of high importance.
Edit: I should point out that this is already somewhat in place. The US dollar, a fiat currency, is currently the world reserve currency, and it’s managed by the US federal reserve central bank. The problem is, the US federal reserve is the US central bank and it is not neutral, nor is it accountable to the rest of the world.