Quine GpT

It doesn't know its own code, but I guess it has the tools to build itself, assuming it has access to documentation of the primitives.

It should technically be able to reproduce its own code

ChatGPT output: "I am not sure which specific programming languages or libraries were used to train my language model, as I do not have access to that information. Language models are typically trained using a combination of various programming languages and tools, and the specific technologies that are used can vary depending on the specific model and the research team that developed it. I am a large language model trained by OpenAI, and I use artificial intelligence (AI) and natural language processing (NLP) techniques to generate responses to text-based queries."

Why do you think this? I don't think there's any reason it would be able to reproduce its own code. It's never seen it so it's not in the weights, and it doesn't have that type of reflection so it can't look it up dynamically.

Give an infinite number of ChatGPTs writing code an infinite amount of time and they will write a ChatGPT

perhaps a little more general, like code for a code optimizing AI chatbot, [with runtime code editing and compilation features ?]