It means that, in order to send a note, your client must do some computational work, and present as evidence a proof with your note. It has potential to reduce spam, since it introduces a cost to sending notes. That cost is measured in computational power.

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It's optional like most nips

What does Pow 2 or 3 or 4 means?

Probably has to do with the amount of computational power put into the note. Potentially the number of leading zeros in a hash somewhere. I assume it can be interpreted as higher numbers = more work.

Could let clients set a threshold to only see notes with some amount of work attached.

The amount of bits equal to zero in the hash of the note.

And not all my notes are having POW written. Is this normal?

Yep, i will remove anything that is under PoW-8 because it's just luck at that point.

Does Amethyst produce PoW events?

Not yet

Planned?