Schrödinger’s Cat Still Lingers on the Mat

The faculty of language can be modeled as an algebraic cycle between a lexicon—an Abelian Hilbert space 𝓗2 spanned by the diagonal matrices of a discrete group we call the Chomsky-Pauli group (GCP)—and a derivational workspace, realized as a Fock-lifted sector 𝓗4 in which syntactic chains arise as tensorized, separable superpositions. Results are three enumerable constraints that jointly identify the grammatically well-formed chains: (i) a rank-1 compressibility condition on chain contexts (satisfied by 96 of the possible matrix sums), (ii) a spectral condition on four-term chain aggregates (satisfied by 32 of those 96, each yielding spectral radius 2φ (twice the golden ratio)), and (iii) a hermiticity condition that restricts the observable subclass to interface-interpretable configurations. The spectral radius emerges as the algebraic fingerprint of X’-theoretic phrasal topology, connecting the lexical group-theoretic structure to a Fibonacci-like growth pattern of language phrase structure. The mathematical claims are finite and exhaustively checkable, and their linguistic interpretation constitutes a program of empirical hypotheses.