Polynomial in terms of what? It's linear in terms of the current hash rate. 'Polynomial' implies some kind of direct assault on the protocol with difficulty not based on other actors.
And 'forking the blockchain' is also misleading. You can fork the blockchain with even the smallest slice of power just by always working on the previous block instead of the current one. The proper explanation is that if you have 40% of the power you have a 1/2 chance of forking a 6-block-old transaction. This does not scale in any unexpected way. If you wait 12 hours for a transaction then it becomes nearly impossible to fork with a minority of the network. This is not a clever insight in any way. It's obvious that since blocks are randomly timed that there is no sharp transition between 49% and 51% between no control and total control. So an attacker only needs to get close to 50%. This barely changes the math wrt taking over the network. Perhaps it adds a factor of two, being generous.
And 'forking the blockchain' is also misleading. You can fork the blockchain with even the smallest slice of power just by always working on the previous block instead of the current one. The proper explanation is that if you have 40% of the power you have a 1/2 chance of forking a 6-block-old transaction. This does not scale in any unexpected way. If you wait 12 hours for a transaction then it becomes nearly impossible to fork with a minority of the network. This is not a clever insight in any way. It's obvious that since blocks are randomly timed that there is no sharp transition between 49% and 51% between no control and total control. So an attacker only needs to get close to 50%. This barely changes the math wrt taking over the network. Perhaps it adds a factor of two, being generous.