The Ultimate Number Domain of Complex Numbers: Fieldoid F; Higher-Order Categories and the Structural Ontology of the Self-Referential Universe
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| Natura: | Recurso digital |
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2026
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| _version_ | 1866901244939862016 |
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| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19325452 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Ultimate Number Domain of Complex Numbers: Fieldoid F; Higher-Order Categories and the Structural Ontology of the Self-Referential Universe zhou, changzheng zhou, ziqing Self-referential depth; Higher-order categories;-categories; Logical depth; Information potential difference; Structural ontology; Quantum phase transition; Topo logical order <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> |
| title | The Ultimate Number Domain of Complex Numbers: Fieldoid F; Higher-Order Categories and the Structural Ontology of the Self-Referential Universe |
| topic | Self-referential depth; Higher-order categories;-categories; Logical depth; Information potential difference; Structural ontology; Quantum phase transition; Topo logical order |
| url | https://doi.org/10.5281/zenodo.19325452 |