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Proof of stake cannot be decentralized since it's permissioned by stake and not permissionless - we studied it since it first thought about in 2014. You literally cannot get stake without someone giving you permission because it's an internally already owned resource. Permission is barrier to entry of up to infinity and another word for censorship. If control is not distributed without permission to independent parties, it cannot be called decentralized nor censorship resistant.

There is no alternative to proof of work because that uses an EXTERNAL permissionless resource available all over the universe for a reason. And it does it in a matter that's provable via a concept known as unforgeable costliness.

Not only is mining permissionless, it's costly to everyone. At equilibrium the mining costs force miners to sell virtually all coins and depend on the markets for recovering those sunk costs just to break even. That means miners are literally forced to give up control to the markets and makes the coins equally accessible without permission via mining or buying on markets forced through unforgeable costliness. The markets, and coin owners, get to price incentives that pay miners on every possible version of the chain preventing many issues including miner collusion that could render sunk costs unrecoverable.

Proof of stake is opposite - it literally forces a permission be given by every token put up for sale, something they never have to do. Staking rewards literally incentivize opposite of distributing control to others by giving you rewards in form of more coins and more control without any additional costs forever.

Proof of work is the most efficient way, the only known way, and the best known way to decentralize control. And it uses far less energy than entire countries regularly use to secure their currency, all in adversarial environment.

The biggest challenge for real decentralized cryptocurrencies is lack of education and enormous incentives to deceive and miseducate everyone for profit. This is why there's so much money these days spent marketing scams that pretend to be cryptocurrencies but are centrally premined (literally skipped permissionless mining for majority for permissioned centrally pre-mined coins) or trivially printed authority token designs like proof of stake all completely permissioned.



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