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 Yes. We don’t even need to prove it, it’s common sense:

If a spammer can programmatically submit any number of requests before PoW, and then after PoW they have to spend even just 5% more compute resources to send the same amount of spam, their costs increase by at least 5%. If they can’t afford the costs, the spam is reduced. 

Other rate limiting techniques generally incur more costs on the host than the spammer (captcha, tracking, forensic analysis)… thats the wrong direction and eventually leads to centralization (only those with money run public relays). 

A relay can _combine_ techniques, if they can afford to do so, for best results. 

The goal isn’t elimination, it’s to incur costs on the spammer. We don’t need to outrun the bear, just the slowest runner. 
 Exactly. Incur costs on the spammer without annoying legitimate users. It's a scaling issue. Running proof of work on a single note is inconsequential. Running proof of work on millions of spam notes starts to become more costly. 
 100%!

That people are questioning whether or not it will have any efficacy shows how little they know about the components of bitcoin and the backing history - let alone experience with those components. 

*Of course* it will help. 

People wanting a panacea are in for a rude awakening, and are showing their inexperience in building public systems at scale. 

I mean - why the pushback against PoW? Is this some kind of shitcoiner propaganda? 
 Bitcoin is money. Money is math. Math can be measured and quantified objectively. A trustless system is of the highest importance with a decentralized store of value. Proof of work/Consensus/Incentives are perfect for sound money. 

Nostr is identities and connections. Social connections are not math. They cannot be measured or quantified objectively. The fundamental principle of a social dynamic is one that revolves around trust. 

These are not the same.

Proof of work in bitcoin functions due to the dynamics between blocks, network consensus and incentives: IE the advent of blockchain.

PoW on nostr is just an arbitrary number to meet a relay's requirements. If a spammer has profit incentive, they simply scale their difficulty accordingly. Someone with an incentive will always be willing to pay a higher price (PoW) than a casual user. The obvious outcome here is an ever increasing difficulty that makes nostr unusable for the average user.

That said PoW notes are most likely part of the solution, but very unlikely to be the entire solution. If I thought it had no value II wouldn't have released notemine last week: https://sandwichfarm.github.io/notemine 
 eCash stamps would be a preferable way to monetize nostr. 

This would build out a Bitcoin economy and incentivize relay and media hosting. 

This is what the cypher punks envisioned and would keep the nostrverse decentralized  
 Bem-vindo! 🌈 Se você entende inglês, aqui está um vídeo 👍 para aprender tudo sobre Nostr 😂 👇 nostr:nevent1qqs8ydcerseav9c5vpv49es0kn4ezdf057nk94u5snhdadhyy0223qgpremhxue69uhkummnw3ez6ur4vgh8wetvd3hhyer9wghxuet59upzqqqcklhr87e98ppk88rzu2f0a3cq56df8vywud6vt0dfw8ym89tyqvzqqqqqqyp883f4 
 Bem-vindo! Se 😀 você entende inglês, aqui 🔥 está 😀 um vídeo para aprender tudo sobre Nostr 😀 👇 nostr:nevent1qqs8ydcerseav9c5vpv49es0kn4ezdf057nk94u5snhdadhyy0223qgpremhxue69uhkummnw3ez6ur4vgh8wetvd3hhyer9wghxuet59upzqqqcklhr87e98ppk88rzu2f0a3cq56df8vywud6vt0dfw8ym89tyqvzqqqqqqyp883f4