yes, "security budget", find revenues for miners. Bitcoin is not a stock, there is no such thing as a "security budget". Network fees are miners problems, its a free market. Bitcoin hashrate/security follows price, that means it will always find a balance and be adjusted according to Bitcoin Market Cap. That balance will always exist.
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Hashrate follows “dollar per block” and not price
In few halving, no matter how big the price is, dollars per block will be significantly reduced unless we get a surge of onchain demand (so far that doesn’t look to be the case) hence enabling trustless bridges will create bigger demand on block which will utilmately generate more dollars per block so hashrate will follow
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dollars per block depends on bitcoin price, you can have full blocks, if bitcoin price crashes, dollar per block crashes, the big gains is still the coinbase reward and it depends on usd price, we have seen hashrate going up with almost empty blocks, because price was up.
Bitcoin network rewards does not need to double after a halving, neither does Bitcoin price, there is no requirement for that, hashrate will always be balanced according to price.
And your solution is no guarantee that demand will come, even because with bigger blockspace fees will be lower.