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Where can I get the source code?

I don't know if the source code has been released, but I think the company funding the research has published an API: https://developer.algorand.org/docs/installing-mac

How can it both claim decentralized trust and be closed-source?

(I work for Algorand) The project will be open-sourced prior to the public launch of the network.

When will the launch happen?

When it’s ready.