Spectral-Inertial Semantics: The Holographic Nyquist Limit and Axiom Conservation in Autoregressive Manifolds

Large Language Models (LLMs) demonstrate emergent reasoning capabilities that defy explanation by classical frequentist statistics. Current interpretations, which treat "hallucination" as stochastic noise, fail to account for the structural coherence and repeatability of these errors. In this paper, we present a unified physical theory that derives the Transformer architecture from first principles as a Symplectic Integrator governing particle motion on a high-dimensional Riemannian manifold. We identify two fundamental laws governing semantic reliability. First, we prove the Semantic Nyquist Theorem, demonstrating that hallucination is a deterministic spectral aliasing artifact when the prompt bandwidth (Bp) falls below the intrinsic curvature of the target concept (2κ). Second, we establish the Law of Axiom Conservation, utilizing Kolmogorov complexity to prove that information deficits inevitably trigger "Axiom Smuggling"—the fabrication of spurious entropy to satisfy thermodynamic constraints. To operationalize these findings, we propose a Low-Rank Inertial Projection method that estimates the falsifiability of generation with O(N) complexity, bridging the gap between rigorous physics and zeta-scale engineering.