Censorship Resistance Property
Resistance to censorship is a consequence of transaction fees. Censorship enforcement is indistinguishable from soft fork enforcement, with majority hash power rejecting non-censoring blocks. Without such enforcement transactions are confirmed on an economically-rational basis despite individual miner subjectivity.
A majority miner is financially profitable. As such there is no cost to acquiring the means of censorship. As mining is necessarily an anonymous role it is always possible for any actor to acquire and deploy majority hash power, and to control it at any given time. As shown in Proof of Work Fallacy, hard forks cannot be used to selectively evict the censor and instead accelerate coin collapse.
In the case of active censorship, fees may rise on transactions that fail to confirm. This fee premium creates a greater potential profit for miners who confirm censored transactions. At a sufficient level this opportunity produces additional competition and therefore increasing overall hash rate.
If rising non-censoring hash power exceeds that of the censor, its enforcement fails. The censor is thus faced with the choice of subsidizing operations or abandoning the effort. Only the state can perpetually subsidize operations, as it can compel tax and gains from preservation of its own currency regime. The state must consume taxes to at least the level of the fee premium to maintain censorship enforcement.
A coin without integrated fees would either fail to a censor or evolve a side fee market. As shown in Side Fee Fallacy it is not necessary that fees be integrated, however fee integration is an important anonymity technique. In either case censorship resistance arises only from the fee premium. The subsidy portion of the block reward does not contribute to censorship resistance because the censor earns the same subsidy as other miners.
It is possible that censorship enforcement could result in a price collapse, causing the censor to incur a loss on operations. However in this case its objective has been achieved, with no opportunity for the economy to counter the censor. This collapse might be achieved at negligible cost by simply demonstrating the intent to censor. It is also possible that a censorship soft fork could lead to a price increase, as white market business embraces the associated state approval. Nevertheless, for the coin to survive, its economy must continue to generate a fee premium sufficient to overpower the censor.
It cannot be shown that the economy will generate sufficient fees to overpower a censor. Similarly, it cannot be shown that a censor will be willing and able to subsidize operations at any given level. It is therefore not possible to prove censorship resistance. This is why resistance to state control is axiomatic.