The Necessity of the Information Axiom and the Octonions D; Existence and Uniqueness Theorem: The Inevitable Emergence of Non-Associative Gauge Fields from Information Axioms
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2026
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| _version_ | 1866901251974758400 |
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| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| contents | <p>Starting from the two fundamental axioms of information conservation and<br>computability, this paper rigorously proves the existence of a unique ∞-groupoid<br>structure that simultaneously satisfies all physical self-consistency conditions. The<br>objects of this ∞-groupoid correspond to information states at different coarse<br>graining scales, and the morphisms are generated by information transitions induced<br>by quantum relative entropy. Through the analysis of the self-referential recursive<br>structure, we prove that this structure inevitably induces an action of a discrete sub<br>group of the modular group SL(2,Z), thereby forcing the information potential dif<br>ference between semantic layers to satisfy a scaling relation, with the scaling factor<br>uniquely determined by modular invariance and the information conservation axiom<br>as λ = e2π. On this basis, the category generated by the tensor product closure of<br>semantic layers is proved to be a modular fusion category, whose minimal non-trivial<br>quantum dimension is the golden ratio ϕ. Combined with the holographic entropy<br>bound Stotal ≈ 10122 nat, the critical depth Nc = 3 is uniquely determined. In the<br>low-energy limit, the space of 2-morphisms forms a finite-dimensional divisible alter<br>native algebra, which Zorn’s theorem restricts to four possibilities: R,C,H,O. The<br>irrationality of the quantum dimension uniquely excludes the first three, thereby<br>forcing an isomorphism to the octonion algebra O. The automorphism group G2 of<br>the octonion algebra reduces to SU(3) × SU(2) × U(1) via spontaneous symmetry<br>breaking in the low-energy limit, and the gauge action consists of a Yang-Mills term<br>and a non-associative topological term, whose coefficient is uniquely determined by<br>the axioms. This paper completes a closed deductive loop from information ax<br>ioms to non-associative gauge field theory, providing a first-principles foundation<br>for understanding the emergence of spacetime geometry and matter fields.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19377632 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Necessity of the Information Axiom and the Octonions D; Existence and Uniqueness Theorem: The Inevitable Emergence of Non-Associative Gauge Fields from Information Axioms zhou, changzheng zhou, ziqing Information Conservation; Computability; ∞-Groupoid; Octonions; Non Associative Gauge Field; Existence and Uniqueness Theorem; Modular Fusion Category; Critical Depth; Three Generations of Fermions <p>Starting from the two fundamental axioms of information conservation and<br>computability, this paper rigorously proves the existence of a unique ∞-groupoid<br>structure that simultaneously satisfies all physical self-consistency conditions. The<br>objects of this ∞-groupoid correspond to information states at different coarse<br>graining scales, and the morphisms are generated by information transitions induced<br>by quantum relative entropy. Through the analysis of the self-referential recursive<br>structure, we prove that this structure inevitably induces an action of a discrete sub<br>group of the modular group SL(2,Z), thereby forcing the information potential dif<br>ference between semantic layers to satisfy a scaling relation, with the scaling factor<br>uniquely determined by modular invariance and the information conservation axiom<br>as λ = e2π. On this basis, the category generated by the tensor product closure of<br>semantic layers is proved to be a modular fusion category, whose minimal non-trivial<br>quantum dimension is the golden ratio ϕ. Combined with the holographic entropy<br>bound Stotal ≈ 10122 nat, the critical depth Nc = 3 is uniquely determined. In the<br>low-energy limit, the space of 2-morphisms forms a finite-dimensional divisible alter<br>native algebra, which Zorn’s theorem restricts to four possibilities: R,C,H,O. The<br>irrationality of the quantum dimension uniquely excludes the first three, thereby<br>forcing an isomorphism to the octonion algebra O. The automorphism group G2 of<br>the octonion algebra reduces to SU(3) × SU(2) × U(1) via spontaneous symmetry<br>breaking in the low-energy limit, and the gauge action consists of a Yang-Mills term<br>and a non-associative topological term, whose coefficient is uniquely determined by<br>the axioms. This paper completes a closed deductive loop from information ax<br>ioms to non-associative gauge field theory, providing a first-principles foundation<br>for understanding the emergence of spacetime geometry and matter fields.</p> |
| title | The Necessity of the Information Axiom and the Octonions D; Existence and Uniqueness Theorem: The Inevitable Emergence of Non-Associative Gauge Fields from Information Axioms |
| topic | Information Conservation; Computability; ∞-Groupoid; Octonions; Non Associative Gauge Field; Existence and Uniqueness Theorem; Modular Fusion Category; Critical Depth; Three Generations of Fermions |
| url | https://doi.org/10.5281/zenodo.19377632 |