Is it possible for the network to "know" hash rate?

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I wanted to know if it was possible for a proof of work network to know its hash rate.
Let’s say a coin was minted based off of the hashrate.

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Ethereum? No, the network switched to PoS a few months ago.

PoW networks in general? Yes, it’s certainly possible to derive it from the difficulty (which is roughly proportional to the log of the hash rate).

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