The steps to run the network are as follows: 1. New transactions are broadcast to all nodes. 2. Each node collects new transactions into a block. 3. Each node works on finding a difficult proof-of-work for its block. 4. When a node finds a proof-of-work, it broadcasts the block to all nodes. 5. Nodes accept the block only if all transactions in it are valid and not already spent. 6. Nodes express their acceptance of the block by working on creating the next block in the chain, using the hash of the accepted block as the previous hash.The word 'invalid' is used in the same context in the 'Calculations' section of the white paper. Specifically, it states;
We consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. Nodes are not going to accept an invalid transaction as payment, and honest nodes will never accept a block containing them. An attacker can only try to change one of his own transactions to take back money he recently spent.In this context 'valid' and 'invalid' is referring to the validity of individual transactions that have been published into a block. For example a transaction's outputs cannot spend/total more than its combined inputs. This meaning of 'valid' is well understood so I will not discuss this further.
The incentive may help encourage nodes to stay honest. If a greedy attacker is able to assemble more CPU power than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth.In this context Satoshi is talking about the fact that by undermining bitcoin and the blockchain by trying to steal from it, he is devaluing his own spoils. i.e. there is a disincentive to try and attack the network. This is unfortunately not a well understood concept but is not relevant to the word 'validity' in terms of hard forks.
While network nodes can verify transactions for themselves, the simplified method can be fooled by an attacker's fabricated transactions for as long as the attacker can continue to overpower the network. One strategy to protect against this would be to accept alerts from network nodes when they detect an invalid block, prompting the user's software to download the full block and alerted transactions to confirm the inconsistency.In this context, an 'invalid' block is simply a block that contains invalid transactions (as discussed earlier in this article) that are being used by an attacker to steal funds. This only works on an SPV (simplified payment verification) node because they do not have the full blockchain to check against. As this is not relevant to the 'validity' of network forks it is outside the scope of this article.
They vote with their CPU power, expressing their acceptance of valid blocks by working on extending them and rejecting invalid blocks by refusing to work on them. Any needed rules and incentives can be enforced with this consensus mechanism.The absolutely key word in these sentences is 'vote'. The mining nodes in the network vote in every block by accepting blocks they consider 'valid' and rejecting blocks they consider 'invalid'. Well this then begs the question; if the miners are voting on what is invalid and what is valid, what determines the validity? This is the crux of the issue. The currently held misunderstanding, often purveyed by a number of Core developers is that validity is determined by whether the blocks fit within the current consensus protocol. This is nonsensical. With each block being a vote, this would be the equivalent of when Fifa had a vote for their president in 2011 and the only name on the ballot paper was Sepp Blatter. In fact it is worse than that, as in the case for bitcoin it would be the same name (rules) on the ballet paper for every single block forever. Just like Fifa, this would make bitcoin into a kind of banana republic where the vote is totally meaningless, and in reality, there is no vote at all. This is in total contradiction to the white paper. In fact what it states is "Any needed rules and incentives can be enforced with this consensus mechanism." This means that the rules can be changed and voted upon if the majority of the hash power agrees.
The proof-of-work also solves the problem of determining representation in majority decision making. If the majority were based on one-IP-address-one-vote, it could be subverted by anyone able to allocate many IPs. Proof-of-work is essentially one-CPU-one-vote. The majority decision is represented by the longest chain, which has the greatest proof-of-work effort invested in it. If a majority of CPU power is controlled by honest nodes, the honest chain will grow the fastest and outpace any competing chains. To modify a past block, an attacker would have to redo the proof-of-work of the block and all blocks after it and then catch up with and surpass the work of the honest nodes.The first sentence "The proof-of-work also solves the problem of determining representation in majority decision making." directly links to the statement in the white paper conclusion that "Any needed rules and incentives can be enforced with this consensus mechanism.". What is being stated is that the rules of the system, and any changes to them, can be determined and enforced using the proof-of-work system. It is stating that the majority of the hash power decides their representation in decision making.
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