This paper identifies a fundamental architectural vulnerability in Context Engineering for Large Language Models (LLMs): the introduction of multiple compression layers that compound error rates in complex, tool-augmented systems. We demonstrate that LLMs are inherently lossy compressors, and Context Engineering—through Retrieval-Augmented Generation (RAG), tool integration, and memory systems—introduces additional runtime compression layers. Each layer creates compression artifacts that interact with and amplify errors from previous layers, analogous to JPEG re-compression degradation. Key contributions: Formalization of the "Layered Compression Paradox" Mathematical framework for error propagation across compression layers Analysis of five critical failure modes including Contextual Sycophancy Proposal of Neurosymbolic Bypass as an alternative architecture