This piece sketches a framework for modeling the language faculty as an algebraically implemented physical system grounded in Fourier duality. Drawing on insights from phonology, syntax, and neuroscience, the approach treats lexical categories as unitary 2 × 2 matrices (the “Chomskys”), whose projections into derivational space (the “Paulis”) preserve information across domains. By leveraging the Fourier transform to relate temporally localized neural events to spatially distributed representations, the system models syntactic composition as operations on conserved, observable states. This allows for a treatment of lexical access with implications for neurophysiological plausibility across oscillatory bands. Extending beyond phonological organization, the model presents a syntax graph and a candidate “Chomsky/Pauli group” (GCP) that capture combinatorial constraints. Lexical items are treated as encrypted roots, recoverable through matrix scalings that correlate with cortical activation dynamics. The synthesis of signal theory, linguistic computation, and neural architecture attempts a path toward understanding how language is physically instantiated in a high-dimensional cognitive system without external supervision.