Schrödinger’s Cat Still Lingers on the Mat
- 1Quantum Department, Donostia International Physics Center, 20018 San Sebastian, Spain
- 2Linguistics Department, University of Maryland, College Park, MD 20742, USA
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.
Related
- Hypergraphs with the smallest Hall ratio are still hard to colour
- Why Constrained Updates Still Forget: A Functional-Path Analysis of Continual SFT
- textGrain watermarking is harder to detect: can sum-tests still do it optimally?
- KATO POTENTIALS AND SCHRÖDINGER OPERATORS ON LIE GROUPS
- Uniqueness and structure-preserving numerical simulations for an Ultrahyperbolic Schrödinger equation
BibTeX
@article{orus2026schrödingers,
title = {{Schrödinger’s Cat Still Lingers on the Mat}},
author = {Román Orús and Juan Uriagereka},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14214037},
url = {https://www.mdpi.com/2227-7390/14/21/4037},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Schrödinger’s Cat Still Lingers on the Mat
AU - Román Orús
AU - Juan Uriagereka
PY - 2026
DA - 2026/11/04
JO - Mathematics
DO - 10.3390/math14214037
UR - https://www.mdpi.com/2227-7390/14/21/4037
AB - 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.
SN - 2227-7390
ER -