Han, Huiwen: Semantic Entropy and Structural Invariance in LLM-Mediated ExpansionCompression Loops

We develop a quantitative information-theoretic account of semantic decay in large- language-model (LLM) mediated ExpansionCompression (EC) loops. Building on the unied framework of DECO Paper 0 (Han, 2026a), we introduce semantic en- tropy HS(X) as the dierential entropy of a random variable distributed over a semantic manifold, and prove that each application of the EC-transform T = C ◦ E is a strictly entropy-reducing operation in expectation (Semantic Entropy Collapse Theorem). We derive clo