Forks don't last more than few blocks because the miners won't get paid. But I think GP raises a fair point that if the idea here is that we are broadcasting the current chain to places that have no other connectivity, then you have to trust that broadcast. By definition you don't have access to other peers to check.

So if you imagine blockstream as an attacker, they could broadcast their version of the chain which say doesn't include payments they made on the main chain so that they could "double spend" them in places that rely solely on the satellite for truth.

Or am I missing something?

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edit: I guess there's no way for blockstream to create blocks at the appropriate difficulty level fast enough, so it would be pretty obvious if they were trying to create their own fork. So I guess this does work..