also the block chain removes central management

How does your scheme prevent the original buyer to continue reusing the same proof of work instead of doing the work ? The same for any party that receives a copy ?

You're effectively turning each transaction into a separate block? This will lead to the problem of block chain splits like we have now, on the level of transactions.  You'd have to redo the work if your transaction was ignored by others. As the frequency of transactions increases, this problem would become worse, up to the point were it is hardly possible to get any transaction through.

There is no block chain, there are no splits and I have read the white paper, I have written my own 'block chain based' multi-currency program, and otherwise am 100% aware of how and why bitcoin works like it does.

My proposal only 'makes no sense' at first, but here is what we already know.

1) People will find hashes for 0.0000793/share or $0.002/share on deep bit.
2) As a merchant, if I gave you work I got from deepbit and you solved it for me then I would earn $0.002/share and no 'block chain' or public 'transaction' was required.
3) As a customer, you are lucky to have enough CPU power to generate $10/day.  However deep bit has enough CPU power to generate $100,000/day.
4) If the customer had a means to hire deepbit (or some other mining pool) to do work for them then the customer could easily 'pay' for anything at a rate of $100,000/day.
5) The demand for a 'transfer medium' would bid up the available GPU cycles in order to accelerate transactions or support 'more' transactions.
6) This will cause the price for mining to go up until there is enough mining available to meet market demand for a medium of exchange and would stop when it was no longer profitable to mine on behalf of others.

No double spending, just like there is no 'double mining'.  
All work exchanges are P2P.  All 'conversions to local currency' can be with trusted peers.  

It is simply a commodity money and the supply is limited in the same way the supply of gold/silver is limited.  It takes work.

The money supply is not 'inflationary' in the 'money from nothing debasement way' because no one can ever 'store' work except as an IOU of the form, "you generated a share for me today, I will generate a share for you tomorrow".  You cannot store a 'pre-computed result' and ultimately, most people would opt for 'I will generate a share for $0.0x' and you credit my account with $ or gold or silver or what ever other item you will pay me with.  In the future you would charge me the going rate to generate a share for me.

So the currency would be 'inflationary', but inflation only matters when people can 'create something from nothing', in this case inflation can only occur by adding more CPU power which is hardly free and all such additional CPU power further secures the value of proof of work because the work becomes more and more 'scarce' for the individual even as it becomes more available as a society.  This drives demand to purchase a share of 'current global cpu power' and not a share of previously generated hash numbers.  The hash numbers merely prove that you 'own' a certain amount of CPU power.

The fact that bitcoin has value and that there is a reward for finding blocks is irrelevant to the value/scarcity of GPU power.  Forcing people to acquire GPU power and proving it by having them solve proof of work creates a means of exchanging value.  Merchants simply become 'resellers' of GPU power earning money from one individual and having their customer do the work.  

1) Bitcoin is not about paying for CPU time, but exchanging shares of a limited stock secured by CPU time.
2) The value of having a limited stock secured by CPU time has been proven by bitcoin, and now miners have popped up who pay others to mine for them (pool operators).  This establishes a market value for a mining share which is in turn tied to the market value of a bitcoin.
3) If we start trading in mining shares which have an established market value, eventually bitcoin blocks become irrelevant as the 'demand' for shares outstrips the supply of GPU power and people can exchange 'work'.  

  

 

Lets assume DeepBit + Bitcoin Pool are two 'work exchanges' among many.

DeepBit pays people $0.01 per share solved and Bitcoin Pool will find shares for others at $0.01/share.

Joe wants to buy a computer from amazon.   Amazon goes to DeepBit and gets work for 100,000 shares and asks Joe to do it.

Joe has a beefy mining rig and decides to just do the work and after 2 weeks has done enough work for Amazon to earn a computer and Amazon has sold all of that work to deepbit earning $1000 for Amazon and costing Joe significant CPU/Time/Energy costs.

Now Sam also wants to buy a computer, but does not have a beefy mining rig nor a desire to wait 2 weeks to make payment, so when Sam gets work from Amazon he hires BitcoinPool to solve that work for him.  Now bitcoin pool is currently solving 10,000,000 shares every 10 minutes.  So Sam gets the work done for Amazon in 10 minutes and Amazon has earned $1000 from Deepbit.

After Joe has paid for his computer, he still has his mining Rig and so joins either Deepbit or Bitcoin Pool earning $1000 every two weeks.

AmazonEurope prefers to be paid euros, so AmazonEurope gets work from DeepEuro which pays .0075 euro share.  Sam wishes to buy a computer from AmazonEurope while on vacation, so he gets work from AmazonEurope and hires BitcoinPool in $USD. 

Work is work regardless of who does it.  It is entirely fungible and divisible.     

Actually, the title is appropriate because while bitcoin mining represents an 'initial market', the proof of work has value by itself.  Bitcoin would merely bootstrap it and eventually efficient miners can 'create work from nothing' in order to close the gap between demand for work per hour and the amount of work that can be done in an hour.  If there is only 1,000,000 shares/hour capacity and yet 2,000,000 shares demand then a miner can charge more than he pays and thus create work 'from nothing' and still make a profit.

I don't understand what happens after the first transaction.

You get proof of work from a miner. You send it to a merchant for a real T-Shirt.

You cannot double spend because you need "fresh" proof of work to buy another T-Shirt. Hence block chain is not required.

How does the merchant spend what you gave him? What keeps him from double spending? How about the guy third in the chain. How can he spend the coin but NOT double spend?

If deepbit can give BTC then we need a block chain or he can double spend or he is acting as a bank an you have to trust him. If deepbit gives $USD, where does he get it? From you? If you, why don't you directly pay with $USD. If deepbit gives out 'share credit' he is acting as a bank again and you have to trust him.