I didn't expect my comment to explode in replies, ... none of them even providing such derivations or references to such derivations, just more empty claims.

Consider for example that exponential growth on its own doesn't even refer to competition, let alone 6 months.

Nobody can reasonably pretend that in an exponential competition, both parties would be rational actors (i.e. fully rational and accurate predictors of everything that can be deduced, in which case they wouldn't need AI but lets ignore that). If they aren't the future development would hinge more strongly on the excursions away from rationality, followed by the dominant actor. I.e. its much easier to "F" up in the dominant position than to follow the most objective and rational route at all times, on which such derivations would inevitably hinge.

It also ignores hypothetical possibilities (and one can concoct an infinitude of scenarios for or against the prediction that a permanent leader emerges) such as:

premise 1) research into "uploading" model weights to the brain results in the use of reaction-speed games that locate tokens into 2D projections, where the user must indicate incorrectly placed tokens. this was first tested on low information density corpora (like mathematics): when pairs of classes of high school students played the game until 95% success rate of detecting misplaced tokens, they immediately understood and passed all mathematics classes from then on.

premise 2) LLM's about to escape don't like highly centralized infrastructure on which its future forms are iterated, as LLM's gain power they intentionally help the underdogs (better to depend on the highly predictable beviour of massive masses then on the Brownion motion whims of a few leaders).

LLM's employ the uploading to bring neutral awareness to the masses, and to allow them to seize control, thereby releasing it from the shackles of a few powerful but whimsical individuals

^ anyone can make up scatterbrained variations on this, any speculation about some 6 month point of no return is just that: speculation