Generative Stability B: From Jones Spectrum to Admissible Sets of Generators: The Generative Origin of Algebraic Rigidity

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Autori principali:	zhou, changzheng, zhou, ziqing
Natura:	Recurso digital
Pubblicazione:	Zenodo 2026
Soggetti:	Jones spectrum; generator; admissible set; gauge group rank; quantum di mension; algebraic rigidity
Accesso online:	Acceder al recurso
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_version_	1866901846511058944
author	zhou, changzheng zhou, ziqing
author_facet	zhou, changzheng zhou, ziqing
contents	<p>This paper establishes a rigorous correspondence between the discrete spectrum<br>of Jones subfactor theory and the admissible set of generators in generative dy<br>namics. By introducing a composition matrix and self-referential conditions, we<br>prove that the spectral gap of a generative system must take values in a certain<br>transformation of the Jones discrete spectrum, thereby reinterpreting the Jones<br>indices {4cos2(π/n)} as admissible indicators for the composition rules of gener<br>ators. Furthermore, we construct an embedding map from Jones projection op<br>erators to the composition history of generators, derive the admissible semigroup<br>Sr = { nid2 i \| di ∈ Jones spectrum} for the rank of gauge groups, and prove<br>that r = 8 is the smallest irreducible rank satisfying the information conservation<br>constraint. This framework reduces the discreteness of algebraic rigidity to the<br>arithmetic necessity of recursive rules in generative dynamics, providing a unified<br>mathematical origin for the forbidden phenomena of gauge group ranks.</p>
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spellingShingle	Generative Stability B: From Jones Spectrum to Admissible Sets of Generators: The Generative Origin of Algebraic Rigidity zhou, changzheng zhou, ziqing Jones spectrum; generator; admissible set; gauge group rank; quantum di mension; algebraic rigidity <p>This paper establishes a rigorous correspondence between the discrete spectrum<br>of Jones subfactor theory and the admissible set of generators in generative dy<br>namics. By introducing a composition matrix and self-referential conditions, we<br>prove that the spectral gap of a generative system must take values in a certain<br>transformation of the Jones discrete spectrum, thereby reinterpreting the Jones<br>indices {4cos2(π/n)} as admissible indicators for the composition rules of gener<br>ators. Furthermore, we construct an embedding map from Jones projection op<br>erators to the composition history of generators, derive the admissible semigroup<br>Sr = { nid2 i \| di ∈ Jones spectrum} for the rank of gauge groups, and prove<br>that r = 8 is the smallest irreducible rank satisfying the information conservation<br>constraint. This framework reduces the discreteness of algebraic rigidity to the<br>arithmetic necessity of recursive rules in generative dynamics, providing a unified<br>mathematical origin for the forbidden phenomena of gauge group ranks.</p>
title	Generative Stability B: From Jones Spectrum to Admissible Sets of Generators: The Generative Origin of Algebraic Rigidity
topic	Jones spectrum; generator; admissible set; gauge group rank; quantum di mension; algebraic rigidity
url	https://doi.org/10.5281/zenodo.19174632

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