Han, Huiwen: The Expansion-Compression Loop: A Unified Framework for AI-Mediated Cognitive Decoupling

We introduce a unified formal framework for analysing what we term AI-mediated cognitive decoupling: the systematic separation of cognitive process from cognitive product enabled by large language models (LLMs) operating as expansion and compression agents. We formalise two operators — the expansion operator E and the compression operator C — acting on semantic content, and characterise the composition C ◦ E as a lossy endomorphism on a semantic manifold S. We introduce the Decoupling Propositio