ad hominem
Ooh, you cribbed some Latin words from the Interwebs! Fancy! Too bad you know nothing of logic or rhetoric.
Like appeal to authority, argumentum ad hominem is only an informal fallacy; unlike formal fallacies, there are situations in which these are not fallacious at all. For example, whereas you have repeatedly shown yourself to be willfully ignorant and ineducable, it is not a fallacy to point out that achow101 is an expert (he is) and you are a doofus (you are). He is right. You are wrong. Quod erat demonstrandum.
Thats not the most rigorous proof Ive ever made, but its more than you deserve. So, get lost.
Appeal to authority over a cryptographic reasoning in a trustless system
Do you have any technically and cryptographically sound arguments that may contribute anything to the discussion too ? Up to now, you sound somewhat like the cardinals telling Galileo that he could get lost (or could get burned) because the authority, Aristotle, said that the earth didn't turn and the Pope too said that he was wrong. That's not how science, or any rational reasoning, is done.
Do you have an argument against my essentially mathematical demonstration that the SPV system can only be fooled in those circumstances where:
1) a full node would be fooled too
or
2) the currently ongoing block chain with the highest PoW contains blocks that are false, ie. contain double spendings, but a large majority of miners nevertheless continues to build upon it ?
I indicated where achow101's answer went wrong, namely that the SPV has the block header chain, just as well as a full node has it. He somehow thought that the SPV protocol consisted in just giving one correctly mined block independent of the block header list. But that's not correct. Even an SPV client gets all block HEADERS. If one would only mine one stand alone block, yes that wouldn't be cryptographically secure, and that's essentially what achow101 tells me. But that's not SPV.
The only thing that an SPV node doesn't do, and a full node does, is to see whether the block bodies are correct. Miners are supposed to do that. But an SPV node cannot be tricked in believing a correctly mined block is part of the chain while it isn't, because it wouldn't fit with the header list.
So only two possibilities remain:
1) the header list I obtained is wrong to trick me
or
2) the block is wrong (contains a double spend)
Well, if it is 1), a full node is just as vulnerable ; and this attack is hugely expensive in PoW.
If it is 2) it means that the chain with most PoW has been mining on top of a false block since quite a while.
Hence my statement is proven.