Proof-Of-Work is a Decentralized Clock

You can use this to increase the fee of a transaction after the fact. So, suppose A has a fee of 0.001 in the first transaction, and the current fee needs to be 0.01 . Then, B has this transaction, but no-one will put it into a block, so B hasn't really received his money yet. A could sign another transaction with a higher fee that would send the money back to A. This could happen until the original transaction was actually deep enough in the chain.

But using your situation, B can do the same thing as A. B can create a transaction sending his own 0.999 BTC to another address of his, and include a fee here of 0.019 . In this fee, there is 0.01 to fund this transaction, and another 0.009 to fund the fee A forgot to include. Miners will see this, and include both transactions, and B is guaranteed he has his money.

What is required however it that a timestamp be at least the median of the last 11 blocks.

Mostly the claim that "The Difficulty is Intergalactic" is just flat wrong. Consider a miner on mars with 10% of the hash-rate on earth. Lets say the light delay from earth to mars is 10 minutes (it is 14 on average).

Now, suppose mars has last seen block B_0 and it was mined on earth (as would happen most often due to 90% of the hash rate being there). We will call E_1 the next block found if only earth were to mine, and M_1 the block for mars. Now, mars has two really big dis-advantages. First of all, earth gets to see B_0 ten minutes before mars does. So, earth can start mining a lot earlier. Second of all, when mars does find a block, but earth finds a block 10 minutes later, earth is going to orphan the martian block.

So, if mars has fewer than 20 minutes of advantage over earth, there is a very good chance any block they find won't matter.

Now, I suppose if the hash-rate is more spread-out over multiple planets, and one planet isn't dominating things might work out. But we might also see consensus break down. I might sit down and do the rigorous math on that tommorow, just to see what happens.

(Other minor nitpicks)

> SHA is Memoryless and Progress-Free

Technically false, because memory-less processes have positive probabilty of yielding no block after 2^256 tries, whereas for sha-256 using brute force, this probability is totally 0. I don't think this matters at the current hash-rate though. (our current hashrate covers about (2.5 * 10^-53)% of the entire output space every 10 minutes.)

> Trying a SHA Makes You a Participant

Only if you would actually submit your hash if you found a match. The same holds for the prime-factorization example. If I happen to factor a huge number and tell no-one I haven't contributed.