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| Main Authors: | , |
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| Formato: | Recurso digital |
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| Publicado: |
Zenodo
2026
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| Subjects: | |
| Acceso en liña: | https://doi.org/10.5281/zenodo.19325452 |
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Table of Contents:
- <p>This paper aims to construct a coherent structural ontology framework for un<br>derstanding physical and mathematical systems with self-referential characteristics.<br>The core thesis is that the intrinsic complexity required to describe such systems—<br>the self-referential depth” (s)—has a strict constructive correspondence with the<br>dimension of higher-order categories. As a system evolves, the accumulation ofin<br>formation potential difference” () drives the dimensional expansion of the categori<br>cal structure describing it. Within this framework, traditional number fields (such<br>as the complex number field ) are reinterpreted as stable projections of infinite<br>self-referential structures (-categories) onto the lowest-order cognitive truncation (<br>category), rather than being the ultimate ontology of physical reality. As a bridge<br>between theory and experiment, we introduce “logical depth” () as the operational<br>proxy variable for self-referential depth in finite physical systems, and derive three<br>testable physical predictions concerning the specific scaling laws of quantum phase<br>transition critical exponents, decoherence time, and topological order fusion space<br>dimension as functions of . These predictions provide explicit test schemes for veri<br>fying the physical relevance of higher-order categorical structures on platforms such<br>as quantum many-body systems, noisy quantum circuits, and topological quantum<br>computation.</p>