Combinatorial Rigidity in Circumstellar Envelopment Lattices: Deriving Hyper-Structural Resilience via the Intersection Numbers of Resolvable Quasi-Symmetric Designs
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| Format: | Recurso digital |
| Langue: | anglais |
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Zenodo
2025
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| _version_ | 1866901123328114688 |
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| author | Revista, Zen MFC, 10 |
| author_facet | Revista, Zen MFC, 10 |
| contents | <p>Mathematical Applications of Science Fiction</p> <p>We present a rigorous derivation of the structural stability conditions for Type-II Kardashev envelop-<br>ment arrays (Dyson Swarms) modeled as geometric lattices derived from Resolvable Quasi-Symmetric<br>Designs (RQSDs). By mapping the block intersection numbers (x, y) of a design D(v, k, λ) to the<br>stress coefficients of a tensegrity framework, we establish a direct isomorphism between the spectral<br>gap of the design’s Bose-Mesner algebra and the infinitesimal rigidity of the resulting circumstellar<br>lattice. We prove the Central Rigidity Theorem, demonstrating that for a specific class of RQSDs,<br>the resulting lattice LΩ exhibits Hyper-Structural Resilience—a state where the kernel of the rigidity<br>matrix is trivial modulo rigid body motions, even under anisotropic gravitational shear. We further<br>analyze the homological stability of these structures, showing that the first homology group over<br>coefficients in R vanishes, implying a lack of localized failure modes. This monograph serves as a<br>foundational blueprint for the construction of mega-structures capable of withstanding stellar radiation<br>pressure and tidal forces.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18098457 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Combinatorial Rigidity in Circumstellar Envelopment Lattices: Deriving Hyper-Structural Resilience via the Intersection Numbers of Resolvable Quasi-Symmetric Designs Revista, Zen MFC, 10 <p>Mathematical Applications of Science Fiction</p> <p>We present a rigorous derivation of the structural stability conditions for Type-II Kardashev envelop-<br>ment arrays (Dyson Swarms) modeled as geometric lattices derived from Resolvable Quasi-Symmetric<br>Designs (RQSDs). By mapping the block intersection numbers (x, y) of a design D(v, k, λ) to the<br>stress coefficients of a tensegrity framework, we establish a direct isomorphism between the spectral<br>gap of the design’s Bose-Mesner algebra and the infinitesimal rigidity of the resulting circumstellar<br>lattice. We prove the Central Rigidity Theorem, demonstrating that for a specific class of RQSDs,<br>the resulting lattice LΩ exhibits Hyper-Structural Resilience—a state where the kernel of the rigidity<br>matrix is trivial modulo rigid body motions, even under anisotropic gravitational shear. We further<br>analyze the homological stability of these structures, showing that the first homology group over<br>coefficients in R vanishes, implying a lack of localized failure modes. This monograph serves as a<br>foundational blueprint for the construction of mega-structures capable of withstanding stellar radiation<br>pressure and tidal forces.</p> |
| title | Combinatorial Rigidity in Circumstellar Envelopment Lattices: Deriving Hyper-Structural Resilience via the Intersection Numbers of Resolvable Quasi-Symmetric Designs |
| url | https://doi.org/10.5281/zenodo.18098457 |