All that an AI has to do to disprove that claim is pay someone to weigh one orange through fivr. So either your claim is wrong, or LLMs as they exist now are no longer statistical models. Go ahead and move the goal post if you want, my complaint was about your overly broad claim.

So you think that AI increasing the capability of new AI just involves training a new model on the output of the old model? Or are you pretending to be a science?

It's entirely possible to improve current AI using only information available to us right now. Once that well runs dry, current AI is in theory capable of running experiments and training on their results if we give it a harness to do that. This gives it access to new information. Could it succeed doing this? Unclear, but it is capable of trying. How do you think we discover AI improvements? Divine inspiration? No, we follow a relatively simple research loop.