I tiakina i:
| Ngā kaituhi matua: | , |
|---|---|
| Hōputu: | Recurso digital |
| Reo: | |
| I whakaputaina: |
Zenodo
2026
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| Ngā marau: | |
| Urunga tuihono: | https://doi.org/10.5281/zenodo.19377632 |
| Ngā Tūtohu: |
Tāpirihia he Tūtohu
Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
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Rārangi ihirangi:
- <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>