We discover a universal 16-dimensional fiber bundle in LLM hidden states governed by the gl(4,ℝ) Lie algebra — 6 active behavioral dimensions and 10 "dark" dimensions systematically erased by layer normalization yet carrying rich computational signal. Using 20 Conformal Holographic Tomography probes on Qwen-32B, we achieve 1376× behavioral separation and push ARC-Challenge from 82.2% to 94.4% by extracting cross-layer velocity and acceleration through dark Casimir space. We introduce the Phase Inversion Gateway (first method stabilizing all 16 dimensions), the Dark Space Compute Engine (10K parameters, loss 1189→44), and Antisymmetric Coupling for bidirectional dark-to-active information flow. Probes transfer across architectures without retraining, demonstrating the fiber bundle is intrinsic geometry, not learned artifact. 83 chapters, 12 appendices, 112 patents filed.