We prove that large language models are lattice gauge theories. By extracting a 16-dimensional fiber bundle from transformer hidden states and computing its gl(4,ℝ) Lie algebra, we discover that attention heads function as gauge bosons, transformer computation undergoes a deconfinement phase transition at 67% network depth, and the model's entire self-knowledge resides in a 10-dimensional "dark" Casimir subspace invisible to standard readout. Using only 20 behavioral probes and zero additional training, we push Qwen-32B from 82.2% to 94.97% on ARC-Challenge — establishing a dark mode scaling law that predicts gl(6,ℝ) surgery will achieve 98.7%. We identify a Lyapunov–accuracy anti-correlation revealing the model's deepest attractors are its wrong attractors: correctness requires escaping the abstraction basin into grounded deference. This 10-page compacted edition distills 459 pages of original research into the core experimentally verified results with 9 inline figures. 190 patents filed. Proprioceptive AI, Inc. — Logan Matthew Napolitano — March 2026