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Presumably there could be another fork like there was with BTC vs Bitcoin Cash (BCH).

If the discrete logarithm problem turns out to be not so difficult, the entire concept of proof of work is meaningless. There is no patch or fork that can possibly fix that.

Proof of work does not depend on the DLP. It depends on SHA.

PoW is just a filter to prevent denial of service attacks, to ensure that if you're a bad actor, you'll waste electricity to send bogus messages.

But if the DLP is easy, then anyone can fabricate proper ECDSA sigs, and you're not wasting electricity to send bogus messages, you're wasting electricity to send valid messages.

The point I was trying to make is that there is no migration path from ECDSA. You can't fork bitcoin if the DLP is easy. It's just game over. Proof of work becomes irrelevant.

That's just not correct. There are plenty of crypto algorithms already, including hash functions, that are designed to be resistant/resilient against a functional quantum computer. A PoW scheme can use any (well, at the very least many) of them.

[1] https://en.wikipedia.org/wiki/Post-quantum_cryptography

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