astutiumRob
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Would coin 1001 on your computer have exactly the same code/keys or whatever the term is as coin 1001 on my computer?
No.
Also this may be where you are confusing yourself, coins do not have keys - think of it in terms of a safe - the safe has keys, the coins inside do not (indeed the coins are in a 'box' called a block, which does not have a key in the same sense)
The 2nd computer/copy in your example would have the same keys (although you may not know the unlock passphrase) so in theory would be able to do something with the contents of the safe that existed at that point - it is after all a direct replica - although what in isolation is limited.
And as soon as you start expanding that to other devices/miners/wallets/etc through connectivity to do anything practical you get into the 51% consensus limitations.
I'd suggest reading the original whitepaper it does make a lot of this much clearer.