PERTURBATIVE CONTROL OF DIRAC EIGENVALUES IN NON-UNITAL SPECTRAL TRIPLES: ENGINEERING FINITE-RESOLUTION TOPOLOGICAL INVARIANTS WITHIN PLANCK-SCALE C*-ALGEBRAIC LATTICES VIA CYCLIC COHOMOLOGY DESCENTS
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2025
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| _version_ | 1866901584468770816 |
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| author | Revista, Zen MFC, 10 |
| author_facet | Revista, Zen MFC, 10 |
| contents | <p>Mathematical Applications of Science Fiction</p> <p>Abstract. We present a rigorous constructive framework for the perturbative control of the spectrum<br>of Dirac operators associated with non-unital spectral triples (A, H, D). By embedding the non-compact<br>manifold data into a sequence of finite-dimensional C*-algebraic lattices (Planck-scale approximations),<br>we derive explicit bounds on the eigenvalue shifts under inner fluctuations of the metric. We intro-<br>duce the Selene-Dirac Perturbation Series, a convergent expansion in the Banach space of bounded<br>operators, to engineer specific spectral gaps. Furthermore, we establish a descent mechanism in cyclic<br>cohomology, proving that the Chern-Connes character of the perturbed lattice system converges to the<br>topological invariants of the continuum limit in the weak-∗ topology. This provides a mechanism for<br>"finite-resolution" topological protection, with direct applications to error correction in quantum gravity<br>models and topological quantum computing.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18095301 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | PERTURBATIVE CONTROL OF DIRAC EIGENVALUES IN NON-UNITAL SPECTRAL TRIPLES: ENGINEERING FINITE-RESOLUTION TOPOLOGICAL INVARIANTS WITHIN PLANCK-SCALE C*-ALGEBRAIC LATTICES VIA CYCLIC COHOMOLOGY DESCENTS Revista, Zen MFC, 10 <p>Mathematical Applications of Science Fiction</p> <p>Abstract. We present a rigorous constructive framework for the perturbative control of the spectrum<br>of Dirac operators associated with non-unital spectral triples (A, H, D). By embedding the non-compact<br>manifold data into a sequence of finite-dimensional C*-algebraic lattices (Planck-scale approximations),<br>we derive explicit bounds on the eigenvalue shifts under inner fluctuations of the metric. We intro-<br>duce the Selene-Dirac Perturbation Series, a convergent expansion in the Banach space of bounded<br>operators, to engineer specific spectral gaps. Furthermore, we establish a descent mechanism in cyclic<br>cohomology, proving that the Chern-Connes character of the perturbed lattice system converges to the<br>topological invariants of the continuum limit in the weak-∗ topology. This provides a mechanism for<br>"finite-resolution" topological protection, with direct applications to error correction in quantum gravity<br>models and topological quantum computing.</p> |
| title | PERTURBATIVE CONTROL OF DIRAC EIGENVALUES IN NON-UNITAL SPECTRAL TRIPLES: ENGINEERING FINITE-RESOLUTION TOPOLOGICAL INVARIANTS WITHIN PLANCK-SCALE C*-ALGEBRAIC LATTICES VIA CYCLIC COHOMOLOGY DESCENTS |
| url | https://doi.org/10.5281/zenodo.18095301 |