Researchers have proposed a new framework for understanding the limitations of large language models (LLMs). They define a 'deployment boundary' where additional computation can only realize decisions already supported by the deployed information. This boundary is formalized through mathematical concepts such as inherited structural capability and resource-indexed finite realization. The authors show that within a common budget, a successor LLM improves every bounded-loss task exactly when its closed convex finite envelope retains the predecessor's capabilities. This theory turns emergence into a problem of boundary control and compatibility. --- Why it matters: This work matters to AI researchers because it provides a new framework for understanding the limitations of large language models. By formalizing the concept of a 'deployment boundary', the authors provide a tool for evaluating and controlling the emergence of LLM capabilities, which is crucial for developing more efficient and effective models. Source: https://arxiv.org/abs/2608.01548