Instability of Absolute Nothingness J: The Necessity of Modular Structure- From Information Ontology to a Unified Geometric Principle of Higher-Dimensional Algebras
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2026
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| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| contents | <p>This paper proposes the “Necessity Principle of Modular Structure”, arguing<br>that the discrete hierarchical structure of congruence (modular arithmetic) is the<br>deep mathematical skeleton connecting information ontology and normed division<br>algebras. By analyzing the discrete definition of information quantity, the rigid<br>classification of Hurwitz’s theorem, and the recursive closure condition in octonion<br>geometry, we prove that modular invariance is the inevitable mathematical form<br>to avoid ontological nothingness and achieve self-consistency of high-dimensional<br>information. This framework reinterprets the periodicity of Euler’s formula as a<br>special case of low-dimensional modular structure, while the scale factor e2π at<br>the octonion level manifests as a generalized modular invariance under maximal<br>information density.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19425962 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Instability of Absolute Nothingness J: The Necessity of Modular Structure- From Information Ontology to a Unified Geometric Principle of Higher-Dimensional Algebras zhou, changzheng zhou, ziqing modular structure; information ontology; normed division algebras; octo nions; recursive closure; Hurwitz's theorem <p>This paper proposes the “Necessity Principle of Modular Structure”, arguing<br>that the discrete hierarchical structure of congruence (modular arithmetic) is the<br>deep mathematical skeleton connecting information ontology and normed division<br>algebras. By analyzing the discrete definition of information quantity, the rigid<br>classification of Hurwitz’s theorem, and the recursive closure condition in octonion<br>geometry, we prove that modular invariance is the inevitable mathematical form<br>to avoid ontological nothingness and achieve self-consistency of high-dimensional<br>information. This framework reinterprets the periodicity of Euler’s formula as a<br>special case of low-dimensional modular structure, while the scale factor e2π at<br>the octonion level manifests as a generalized modular invariance under maximal<br>information density.</p> |
| title | Instability of Absolute Nothingness J: The Necessity of Modular Structure- From Information Ontology to a Unified Geometric Principle of Higher-Dimensional Algebras |
| topic | modular structure; information ontology; normed division algebras; octo nions; recursive closure; Hurwitz's theorem |
| url | https://doi.org/10.5281/zenodo.19425962 |