> Your argument is not mathematical at all. It assumes first that bitcoin needs to appreciate 10-100 times current value
Satoshi consensus doesn't care about the numeric value of Bitcoin at all. It cares about the value of the transactions conveyed by bitcoin.
Satoshi consensus is the observation that if the energy required to fork the network and roll back a transaction costs $X, then it's financially non-viable for someone to roll back a set of transactions that is worth less than $X. That's all. If the value transacted on bitcoin increases above $X, then it is potentially financially worth it to attack the network, unless the amount of energy expended increases accordingly. So the value of the transactions is directly tied to the (value of the) energy expenditure.
As a side note, there is no automatic mechanism built into bitcoin that ties these two values together. The assumption is that the value increases and the rewards decrease and it all sort of works out (especially if the network transitions to transaction fees instead of inflation-based block rewards). But there is no mechanism that it must, and if the value dropped really hard all of a sudden, for example, it might suddenly be more viable to attack the network. Attacker energy cost will significantly decrease as rational actor miners realize they're taking a loss and turn off their mining hardware, miner energy expenditure will decrease, which decreases the energy (and cost) required for attackers to fork and roll back transactions.
It's an interesting variation of the "frisbee on the roof" attack, like a "fire all the janitors and then shit on the floor" attack. Nobody ever wants to go back into that business because there's shit all over the floor, but without any customers there's no money to hire janitors either. The network now enters a terminally unrecoverable state, without manual intervention from outside actors.
> if the value dropped really hard all of a sudden, for example, it might suddenly be more viable to attack the network
In practice, users of bitcoin would simply wait a longer time for more block confirmations, namely if you estimated the cost of a double spend attack was $X you would just wait for block confirmations with a total of more than $X of fees + block rewards such that the transaction you are confirming is deep enough in the blockchain to not be economical to include in the double spend attack. Note that the slowness of difficulty adjustments is also a defense here against the further problem of $X decreasing very quickly such that a transaction you had already confirmed becomes viable to attack. Because difficulty changes only every 2016 blocks, if all mining stopped and $X theoretically became 0, in practice you won't get to the next difficulty as no new blocks would be found, so $X in practice wouldn't move.
Satoshi consensus doesn't care about the numeric value of Bitcoin at all. It cares about the value of the transactions conveyed by bitcoin.
Satoshi consensus is the observation that if the energy required to fork the network and roll back a transaction costs $X, then it's financially non-viable for someone to roll back a set of transactions that is worth less than $X. That's all. If the value transacted on bitcoin increases above $X, then it is potentially financially worth it to attack the network, unless the amount of energy expended increases accordingly. So the value of the transactions is directly tied to the (value of the) energy expenditure.
As a side note, there is no automatic mechanism built into bitcoin that ties these two values together. The assumption is that the value increases and the rewards decrease and it all sort of works out (especially if the network transitions to transaction fees instead of inflation-based block rewards). But there is no mechanism that it must, and if the value dropped really hard all of a sudden, for example, it might suddenly be more viable to attack the network. Attacker energy cost will significantly decrease as rational actor miners realize they're taking a loss and turn off their mining hardware, miner energy expenditure will decrease, which decreases the energy (and cost) required for attackers to fork and roll back transactions.
It's an interesting variation of the "frisbee on the roof" attack, like a "fire all the janitors and then shit on the floor" attack. Nobody ever wants to go back into that business because there's shit all over the floor, but without any customers there's no money to hire janitors either. The network now enters a terminally unrecoverable state, without manual intervention from outside actors.