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| Asıl Yazarlar: | , |
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| Materyal Türü: | Recurso digital |
| Dil: | |
| Baskı/Yayın Bilgisi: |
Zenodo
2026
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| Konular: | |
| Online Erişim: | https://doi.org/10.5281/zenodo.20360839 |
| Etiketler: |
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İçindekiler:
- <p>Structural openness endows a system with the ability to transform its own con<br>straints at the meta-rule level. However, without rigid boundaries, it leads to the<br>paradoxes of information creation and computational infeasibility. This paper pro<br>poses two fundamental axioms: the information conservation axiom requires that<br>rule transformations do not alter the total amount of discriminative information<br>the system can process, which is equivalent to requiring the corresponding phys<br>ical map to be a doubly stochastic completely positive trace-preserving map; the<br>computability axiom requires that the transformation process be completable by a<br>Turing machine in finitely many steps and that the output rules have finite Kol<br>mogorov complexity, which is equivalent to a Kraus representation of finite rank<br>with computable matrix entries. By introducing a rule-physics two-layer semantic<br>functor, rule transformations are strictly mapped to Heisenberg-picture maps on<br>the projection lattice, thereby establishing an invertible translation between the<br>rule layer and the physical layer. The intersection of the two axioms constitutes<br>the admissible set, which is proved to be a discretely generated monoid. Further<br>more, the fixed-point algebra of a rule transformation yields a subfactor inclusion<br>whose Jones index lies in the discrete spectrum {4cos2(π/n)} and is strictly less<br>than 4, quantising the information twist. Modelling rule recursion as a cascade<br>of hierarchical quantum channels, the Holevo bound gives an upper bound on the<br>decay of information transmission capacity with recursion depth. Three indepen<br>dent paths — information capacity, finite description length, and the discrete Jones<br>spectrum — converge to the same conclusion: the recursion depth must be finite,<br>and its upper bound is locked by the system dimension, computational resources,<br>and the discrete Jones spectrum without any external parameters. This framework<br>transforms the boundaries of structural openness into computable mathematical<br>physical objects.</p>