Please don't make me explain this again. Every since we started discussing Iota, you have continued to repeat this same myopia over and over and over and over and over and over again. It is very redundant and it is cluttering the thread with noise. Whoever can't understand this very simple concept by now, isn't likely to ever understand it.
Partial ordering is a weaker requirement than total ordering, making the statement true. It doesn't matter if it is impossible to achieve in practice; I was making a gross simplification to prove a point, but that appears lost on you.
How many times have I told you that you can not analyze consensus designs piecemeal. It leads to nonsense posts.
Incorrect. You completely failed to comprehend the explanation I made in my prior post. Try reading it again and again and again until you can comprehend.
Nothing in that post addresses the problem. I'll say it again: If you remove the block reward, you remove the honest miners incentive, along with part of the game theory which makes bitcoin work. What incentive is there in your system to play by the rules for an attacker?
I already had explained this and I don't understand why it is so difficult for you to comprehend that the payers must send a PoW with their transactions. The majority of the PoW comes from payers, and the payers have every incentive to approve the longest chain, so their transactions are included on the block chain. If an individual payer wants to attempt a double-spend, he doesn't have enough PoW by himself to accomplish it.
Profitability of mining has nothing to do with the incentives in my design. I hope I don't have to explain this again.
You have shown no such weakness in my current design. Yeah I found flaws in my prior designs. So what. I made it very clear in the past that those designs were still under study and that I was not announcing the details until I was satisfied with my internal review.
Tell me this: how can a recipient know when it is safe to accept a transaction in your design?
Same as in Satoshi's design. When the acceptable number of blocks have been confirmed since the block that included the transaction.
Note that there is another mechanism for instant confirmations as well, but it is optional.
I've already shown you why this statement is incorrect. If you'd like me to go into more detail, I will.
No you have not! Damn it, you make me repeat the same explanations over and over and over and over again.
You continue to make the same mistake over and over: rushing to conclusions. There is no concept of time or clocks whatsoever involved in the tree of work idea, only longest chain of work.
You can't have branches which don't conflict on double-spends without a total ordering. You can't get total ordering without LCR unless you use a clock to timestamp each node of the tree. Period.