Well, it fails on decentralization already, and "asymptotically" means wasting more than half of human's resources.

Because if you are presented with different block chains, and the ethereum block chain contains more proof of economic waste than what people used to call the bitcoin block chain, according to your rule, you have to accept the ethereum block chain as the sole true consensus document

The example detail is a bit confusing. If I understand correctly, you want to buy at an exchange with low rate, and sell at another exchange for a higher rate but the trade closes at a later date. That doesn't seem like a reasonable way to do arbitrage. The waiting part of your trade kills the idea of an arbitrage.

If it is necessary for a system to waste GW of electricity as its fundamental "security" principle, as compared to systems that can be made as economical as technologically possible, there's no justification for that huge waste, which engenders a lot of OTHER problems, like the power concentration (the centralization of decision).

If you're talking about trustlessness, you cannot include hypotheses like this.   After all, this is very well not true, especially when there are possibilities to short bitcoin outside of the system.  It may very well be profitable to kill bitcoin, because, as you say, there's competition in the larger market too.

Because if not, the other half may be used to produce that famous B.   How do you know that in fact, bitmain doesn't have 8 times the amount of mining hardware they have sold on the market, in a secret place somewhere, ready to be switched on to produce a "false" block chain ?  Maybe they get subventions from the Chinese government to screw bitcoin, who knows ? 

Hey, how come that you trust the genesis block ?  Because it is written in software that some dudes signed with their signatures on centralized Github ?  Maybe it is not the right one !  Maybe what that piece of software tells you, is actually not the "true" bitcoin block chain !  Who knows !  You trusted Core's signatures ?

Here's the problem bitcoin's proof of waste tries to solve:

"show me that, amongst X different possible states of consensus, consensus proposal "A" is the unique right one, even if I wasn't there, and even if I don't trust ANYBODY".  Moreover, "show me that just any other entity like me, not trusting anyone, and not having been online when these decisions were made either, will come to the same conclusion that it was A, and not B, even if that other person is presented another collection Y of possible states of consensus.".

Not at all.  Read it.  It is about the amount of waste produced by a successful PoW asset, eating up a significant part of earth's economy in electricity and hardware to produce waste and nothing else.  It has nothing to do with money, but all with Proof of Waste.

BTW, couldn't resist: https://ideas.repec.org/p/edn/esedps/110.html

I would like to draw one's attention to the thread I have elsewhere, which points to a fundamental problem with PoW.  

That is, for the proponents of PoW, what's the vision on that ?

https://bitcointalk.org/index.php?topic=2847680

...However, as the author notes in that second paper above, in it's pure form it offers no protection from sybil attack. The author suggests using stake from another blockchain in order to weight votes to provide some protection again sybil attack, but does not talk about the inherent problems in doing so, such as the transient nature of the balance of any particular staking address in another blockchain.

In addition the author talks about using PoW to acquire voting weight, which does not suffer from the same transient problems associated with stake, but it is still largely PoS in nature since voting weight persists or decays at a finite speed, unlike the way PoW functions in bitcoin, for example.

All in all, I think it has applications outside of cryptocurrency, but IMO is poorly suited to the requirements of the consensus mechanism within one.

For example, you are assuming that in order to arbitrage you must move your coin from one exchange to another - you would be better served to simply worry about the outcome. If you buy low and sell high, why does it matter if you combine the coin?

The difficulty was brought in to prevent one "bad" actor with massive amounts of hashing power to mine all the blocks for himself and also to adapt to the technological improvement of processing power. So as soon as there are a massive spike in the total hashing power, then the difficulty will adjust to balance things out.

The difficulty is one of the core principles of the protocol. ^smile^

This is a very good idea, but it shouldn't be used as a reward to consensus.  I think consensus should be done freely and then PoS is a good method (see other thread).  However, I think PoW is a good technique for coin creation (independent of consensus decision).  If coin creation is proportional to a weighted form of proof of work, where the weight is the economic cost of proof of work (technology dependent), then we have an automatic value control mechanism, and we are finally making a CURRENCY, not a speculative get-rich-by-hodling asset.  That currency would be created more if its market price rose (it is then more interesting to spend PoW to make it, than to buy it in the market).   Coin issuance would stop if the price goes below the cost of PoW.  In other words, PoW would work as the central bank regulating supply, and there's no problem of seigniorage, because it is wasted on PoW.

If a coin is set to cost about, say, $10 in PoW, then that coin will hover steadily around $10.  If it rises, more coins are created and this extra offer plummets the price.  If it drops, no more coins are created and its scarcity can make the price rise again.  Moreover, the expectation of constant price will avoid speculation, and promote currency usage.

But again, one should not reward consensus. 

The market structure does not matter; the strike/price/numbers that you input and output are going to be what matters. Write out everything you plan to do, the prices, the fees, etc. and see if you come out positive, or if you're daring and confident you can just go for it and make the trades/purchases and see if you end up with more money. Either way, you will have your answer, but without more information, criteria and parameters there is no way to respond to your question, except with more questions.

It is a silly idea to want to be able to prove to you that during your absence, everything happened according to the rules.

Order is simply a consensus.  It has not much to do with time.  In fact, transactions don't even need to be time-ordered.  If there are no double-spends, their order is automatic.

But that's all that is needed; order.  Not "real world time".  Of course, IF you tag real world time to transactions, you automatically get an ordering.  And IF you tag real world time to consensus pictures, they are of course also automatically ordered.  But it is not a necessary condition.

In order to avoid this, one needs to make sure that nobody is accumulating hardware capacity without using it.  Bitcoin is only protected if one can make sure nobody has a significant amount of unused hardware.  If one has a huge pile of unused hardware, one can switch it on and outperform the existing system with not much more proof of work than was put into it.

So bitcoin's ultimate protection is not by proof of work, but by proof-of-non-existence-of-unused-hardware.  See, the attack of piling up unused hardware is obvious in PoW.

That really depends on the PoS algorithm.  It would be a stupid algorithm that doesn't allow staking.

You basically mentioned uncle blocks which is used by Ethereum.

While it could reward miners and not wasting resources used to mine blocks, there are some flaws such as :
1. Increasing bitcoin production which could rise maximum bitcoin supply and could cause inflation.
2. It could be abused by miners to earn more coins and my 1st point would happen even worse.
3. While i don't have much info, i'm sure adding uncle blocks will require more computing power to run full nodes which could risk decentralization.

Source :
https://bitslog.wordpress.com/2016/04/28/uncle-mining-an-ethereum-consensus-protocol-flaw/

Yes, and nobody needs that.  One only needs ORDER, not "real world time proxies".  

In proof of work, if you do slightly more work than the "good guys" (that is, the ensemble of miners that were working "honestly"), you won.  It is sufficient that you have proven, say, 50% more hashes than the "good guys" your chain will take over.  With a digital signature, that is not "50% more", but 2^128 times more or so.

They are only vulnerable to attacks from the inside, that is, from their owners, and then it depends exactly on the PoS scheme used.  They cannot be attacked from the outside, from someone who doesn't have any stake in the system and never owned some stash.  As to the exact attacks that are possible, that depends on the precise implementation of the PoS scheme.

PoW can even be attacked with all users offline, because the PoW stake holders have nothing to do with the coin.  If tomorrow, the Chinese government confiscates most of the mining equipment, bitcoin is in the hands of the Chinese government.  With a PoS coin, that's simply impossible.