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 1. The algorithm was designed specifically for @geyser , so that's why there is the condition of donation at the beginning.

The user is donating/replying *to someone*.

As you pointed out, if the user is posting, than there is no donation to someone else, so that can be replaced by a PoW msg.

So smth like:

- if post
    > PoW • c > t
- if reply
    > sats  > t

c is a conversion factor based on the hashrate and issuance of bitcoin. 
 If donation is verified by the platform (geyser) then it's fine (for that platform), although not decentralized - others can't verify the donation was made without trusting geyser and integrating their api. 

PoW is trivial to verify by anyone, and trivial to execute (no need to setup LN wallet etc) - although as mentioned elsewhere - there will be PoW marketplaces which means people who have access to them (and to LN to pay for them) will have several order of magnitude cheaper PoW. Plus that's a burn - it actually boils the oceans for the sake of it. So overall, I think PoW has it's place only for new/anon users with zero reputation (who are ready to "pay" to bootstrap), after that we should use other signals - content and links (trust ranks). 
 yeah, I see your point and I agree.

anon have to prove something, unless their global trust score is > 0