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.

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Publication Details

Journal
Mathematics
Published
2026-11-04
DOI
https://doi.org/10.3390/math14214037
Primary Topic
Syntax, Semantics, Linguistic Variation
Type
article
Field-Weighted Citation Impact
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article

Schrödinger’s Cat Still Lingers on the Mat

Román Orús, Juan Uriagereka
Mathematics
Syntax, Semantics, Linguistic Variation
article

Schrödinger’s Cat Still Lingers on the Mat

Román Orús, Juan Uriagereka
article en

Abstract

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.

MathematicsVol. 14(21)
Donostia International Physics Center (ES), University of Maryland, College Park (US)
Openalex Percentile: Top 4%
Syntax, Semantics, Linguistic Variation
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