"The Cat Sat on the xxx?" Why generative AI has limited creativity

Since the introduction of Generative AI several years ago, there has been much debate regarding the capacity of this technology for creativity. This paper applies the standard definition of creativity to the output of Large Language Models (LLMs) and shows not only that this can be calculated ex ante, but that LLM output creativity has a fundamental upper limit. This upper limit, determined by the mechanism used to produce LLM outputs, moreover, is constrained to a level equivalent to the boundary between little-c and Pro-c creativity. Consequently, LLM creativity is mathematically constrained to a level equivalent to the boundary between amateur and professional human creativity. This has significant implications for claims about AI autonomy in creative tasks.