Is this sentence of Vitalik Buterin correct?
Buterin’s original is incorrect. “... network applies ...” should say “... network that applies ...”, with “that” referring to the previously mentioned assumption.
Your final version seems the best. It removes the redundant and unnecessary “continues to apply”, which adds nothing to the stated reliance on an existing assumption.
The only modification I suggest is to remove “do”, which is not needed. Its only function is to place a little emphasis on the reliance, and I doubt that that emphasis is needed.