As long as you trust a significant portion of your peers to be following the same rules as you, the validitation result of the most recent entry ‘proves’ the validity of all the entries before it.
validitation -> validation
Perhaps I’m being a bit pedantic here, but it would be good to be a bit more quantitative about the assumption of trusting a significant portion, rather than the extreme of validating all transactions. That said, I understand it may be difficult to give a quantitative figure. Edit: actually, I’ve just realized the point, this is customizable according to an agent’s preference of speed of transaction, vs security and finality. I think if there is at least an honest minority, or even at least one honest validator who recursively validates all relevant transactions, it should be possible to expose invalid transactions, broadcast warrants, and then act accordingly depending on the app and context (e.g. blacklist). However, if there is a dependence on at least one honest validator validating all transactions, then that introduces a centralization risk. I guess that there has to be either some level of trust, or to validate all relevant transactions oneself, which can be computationally expensive, and require increasing computational power as the network scales.
I guess that in reality most people will be honest validators, so the above assumption seems safe.