The continuous real number system lacks the necessary dimensions to encode the branching complexity of non-Archimedean geometry. Linear space inherently destroys categorical relationships during the projection process. This mathematical flattening ensures that particles sharing a recent common ancestor appear entirely unrelated in the observable physical domain. https://qnfo.org/releases/2026/03/Topological+Aliasing+and+Holographic+Readout#3.3+The+Loss+of+Categorical+Information+in+Linear+Space