Axiomatic Emergence D; The Physical Origin of Higher-Order Categories
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2026
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| author | zhou, Changzheng zhou, ziqing |
| author_facet | zhou, Changzheng zhou, ziqing |
| contents | <p>This paper is the third part of the research program ”Deriving Mathematical<br>Structures from the Axioms of Information Conservation and Computability.” We<br>prove that in a self-referential discrete quantum dynamical system satisfying In<br>formation Conservation (A1) and Computability (A2), to achieve self-consistency<br>in the multi-scale description of the system’s evolution, its mathematical frame<br>work necessarily extends from an ordinary category to a higher-order category<br>(∞-category) and topological ∞-stack. The core mechanism is that the non<br>commutativity of the system’s ”coarse-graining” operation sequences naturally gives<br>rise to 2-morphisms describing the relationships between different ”computational<br>paths.” Furthermore, the self-referentiality of the system, which implies a decision<br>limit isomorphic to the halting problem, guarantees that this tower of morphisms<br>must extend to infinite higher orders (i.e., forming an ∞-category). The Information<br>Conservation axiom constrains all higher-order morphisms to be reversible ”entropy<br>preserving homotopies.” To coordinate theoretical descriptions from different local<br>observational perspectives, these local ∞-categories need to satisfy global consis<br>tency conditions, thereby naturally organizing into a topological ∞-stack. The<br>geometric structure of this ∞-stack encodes topological information of the physical<br>theory space and leads to a specific, falsifiable cosmological prediction: there should<br>exist a sinusoidal oscillatory modulation with an amplitude of approximately 0.008<br>and a frequency around 10−4 Hz in the primordial gravitational wave power spec<br>trum produced during the early universe’s inflationary epoch. This prediction can<br>be tested by future space-based gravitational wave detectors such as LISA.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18290281 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Axiomatic Emergence D; The Physical Origin of Higher-Order Categories zhou, Changzheng zhou, ziqing Information Conservation; Computability; ∞-Category; Topological ∞ Stack; Renormalization Group; Higher-Order Homotopy; Primordial Gravitational Waves; Cosmological Test <p>This paper is the third part of the research program ”Deriving Mathematical<br>Structures from the Axioms of Information Conservation and Computability.” We<br>prove that in a self-referential discrete quantum dynamical system satisfying In<br>formation Conservation (A1) and Computability (A2), to achieve self-consistency<br>in the multi-scale description of the system’s evolution, its mathematical frame<br>work necessarily extends from an ordinary category to a higher-order category<br>(∞-category) and topological ∞-stack. The core mechanism is that the non<br>commutativity of the system’s ”coarse-graining” operation sequences naturally gives<br>rise to 2-morphisms describing the relationships between different ”computational<br>paths.” Furthermore, the self-referentiality of the system, which implies a decision<br>limit isomorphic to the halting problem, guarantees that this tower of morphisms<br>must extend to infinite higher orders (i.e., forming an ∞-category). The Information<br>Conservation axiom constrains all higher-order morphisms to be reversible ”entropy<br>preserving homotopies.” To coordinate theoretical descriptions from different local<br>observational perspectives, these local ∞-categories need to satisfy global consis<br>tency conditions, thereby naturally organizing into a topological ∞-stack. The<br>geometric structure of this ∞-stack encodes topological information of the physical<br>theory space and leads to a specific, falsifiable cosmological prediction: there should<br>exist a sinusoidal oscillatory modulation with an amplitude of approximately 0.008<br>and a frequency around 10−4 Hz in the primordial gravitational wave power spec<br>trum produced during the early universe’s inflationary epoch. This prediction can<br>be tested by future space-based gravitational wave detectors such as LISA.</p> |
| title | Axiomatic Emergence D; The Physical Origin of Higher-Order Categories |
| topic | Information Conservation; Computability; ∞-Category; Topological ∞ Stack; Renormalization Group; Higher-Order Homotopy; Primordial Gravitational Waves; Cosmological Test |
| url | https://doi.org/10.5281/zenodo.18290281 |