Spectral Selection Rule D: Higher-Order Topological Orders and Composite Spectral Invariants– Cascade Constraints on Viable Universe Models
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2026
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| _version_ | 1866901412887134208 |
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| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| contents | <p>The paradigm of screening universe models based on a single topological invari<br>ant (such as the spectral invariant Z), though illuminating, may fail to exhaust<br>all the constraints imposed by physical reality. This paper proposes that a viable<br>universe must simultaneously satisfy a composite constraint condition composed of<br>multiple independent topological invariants. These invariants originate from the<br>universal topological properties exhibited by physical systems at different dimen<br>sions and different symmetry levels. We take the spectral invariant Z, rooted in<br>chiral anomalies and boundary excitation modes, and the spectral invariant Y ,<br>originated from higher-dimensional generalized symmetries and higher-order Hall<br>responses, as examples to demonstrate that they correspond respectively to the<br>necessary self-consistency conditions for the “observable universe” and the “higher<br>dimensional spacetime structure”. It is particularly necessary to point out that Z<br>and Y are physically independent at their origins but mathematically constrained<br>by the hierarchical relationship strictly determined by the Drinfeld center construc<br>tion– this “determination-screening” dual structure constitutes the rigorous core<br>of the cascade screening mechanism. The combination of the two forms a cascade<br>screening mechanism, which can exponentially increase the screening efficiency and<br>elevate model construction to a new paradigm with greater predictive power.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20091462 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Spectral Selection Rule D: Higher-Order Topological Orders and Composite Spectral Invariants– Cascade Constraints on Viable Universe Models zhou, changzheng zhou, ziqing topological order; higher-order symmetry; spectral invariant; model screen ing; quantum gravity; category theory <p>The paradigm of screening universe models based on a single topological invari<br>ant (such as the spectral invariant Z), though illuminating, may fail to exhaust<br>all the constraints imposed by physical reality. This paper proposes that a viable<br>universe must simultaneously satisfy a composite constraint condition composed of<br>multiple independent topological invariants. These invariants originate from the<br>universal topological properties exhibited by physical systems at different dimen<br>sions and different symmetry levels. We take the spectral invariant Z, rooted in<br>chiral anomalies and boundary excitation modes, and the spectral invariant Y ,<br>originated from higher-dimensional generalized symmetries and higher-order Hall<br>responses, as examples to demonstrate that they correspond respectively to the<br>necessary self-consistency conditions for the “observable universe” and the “higher<br>dimensional spacetime structure”. It is particularly necessary to point out that Z<br>and Y are physically independent at their origins but mathematically constrained<br>by the hierarchical relationship strictly determined by the Drinfeld center construc<br>tion– this “determination-screening” dual structure constitutes the rigorous core<br>of the cascade screening mechanism. The combination of the two forms a cascade<br>screening mechanism, which can exponentially increase the screening efficiency and<br>elevate model construction to a new paradigm with greater predictive power.</p> |
| title | Spectral Selection Rule D: Higher-Order Topological Orders and Composite Spectral Invariants– Cascade Constraints on Viable Universe Models |
| topic | topological order; higher-order symmetry; spectral invariant; model screen ing; quantum gravity; category theory |
| url | https://doi.org/10.5281/zenodo.20091462 |