I'm still not convinced... I have problems with the following:
6) If Satoshi x mints a block on one chain at minute x and sends a txn on a fork at a time x-t, where t>=0, then this satoshi is blacklisted.
So if you send and then mint you get blacklisted. But that doesn't cover all the cases. If I get past ownership of coins that never minted, I can use that to mint in a second chain, at least up to the moment were those coins changed ownership. So I used "past input ownership" to create part of a second chain. By jumping thru different past ownerships I can get very close to the present and accumulate more work in my chain to the point that I might not even need current ownership.
Sorry I didn't read this carefully enough. Mea culpa. My previous answer was wrong. I have edited my answer.
In your example, Satoshi x mints on one chain at time x and sends a txn at time x+t on a second chain. So yes, you are correct.
I should have defined the rule as follows:
Consider minting as a type of txn. Recall that public keys cannot be reused.
If a public key signs two or more txns, then all Satoshi controlled by the public key are blacklisted from the block number of that key's earliest txn and onwards.
That should cover all possible cases.
7) If Satoshi x mints blocks on multiple chains at minute x, then this satoshi is blacklisted.
you say "this satoshi" however there are no satoshis, only ins and outs. You can have colored coins and forbid loss of color, and that would be ok, but unless you color every satoshi (which is not practical), I don't see how you could match one satoshi from one chain to one in another chain. Colored coins can track coins in one chain, but when you have 2 competing forks, it's not that straightforward
It is not difficult to track Satoshi serial numbers. Recall that you cannot send txns that use more than one input. Thus, you can only split inputs into two or more outputs. You can never recombine two or more outputs into one input. This implies that we can record the set of satoshi numbers associated with each output using just two numbers.
e.g. This output contains satoshi 10,000,000,000,000,000 (inclusive) up to satoshi 20,000,000,000,000,000 (exclusive).
Whereas before the blockchain would simply write this output contains 10,000,000,000,000,000 satoshis.
You don't actually have to record any new data in the blockchain. Instead, you can derive the data from the blockchain. Just define the output listed first in a txn as containing the lowest numbered satoshis and scan the blockchain.
Even if you recorded the data directly in the blockchain, the extra space required would be tiny.
The added data would be equivalent to writing the amount of sent coins twice instead of once.
That's like an extra 7-8 bytes per txn, almost nothing.
Finally, I included these rules to provide a simplified example. The rules are restrictive and probably not a sensible arrangement. However, the simplified rules define a long-run consensus. There is no use of checkpoints here (outside of agreement on a common genesis block).
