Structural Isomorphisms between Deformed GUE Kernels, Fractal Fokker-Planck Dynamics, and Open Logical Systems
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| Natura: | Recurso digital |
| Lingua: | inglese |
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2025
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| _version_ | 1866901194185637888 |
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| author | Gutiérrez, Marco Llere |
| author_facet | Gutiérrez, Marco Llere |
| contents | <p>Theoretical physics currently faces a disjointed landscape regarding the modeling of com<br>plex stability: Random Matrix Theory (RMT) assumes universal GUE statistics, stochastic<br>dynamics rely on standard Fokker-Planck evolution, and formal logic grapples with incom<br>pleteness in closed systems. In this work, I present evidence that these three domains share<br>a common, underlying geometric constraint structure: multiscale fractal coherence.<br>First, based on a high-precision spectral analysis (N = 105 Riemann zeros), I report a<br>systematic determinantal asymmetry (∆β ≈ 0.217) that converges asymptotically, suggest<br>ing a structural rigidity not contemplated in the pure GUE model. I model this anomaly via<br>an additive deformation of the sine kernel, induced by a background arithmetic structure.<br>Second, I establish an isomorphism between this deformation and the steady state of<br>a McKean-Vlasov equation with long-range interaction. I show that the dynamic contain<br>ment term acts by penalizing fine fluctuations, generating increasing rigidity in the system<br>analogous to spectral viscosity.<br>Third, I formalize the conservation of this structure using Topos Theory, defining the<br>aperture operator L as a functor that preserves functional coherence Φ across a hierarchy<br>of systems.<br>I propose that the spectral deformation parameter γ, the dynamic containment coefficient<br>λ, and the logical aperture degree κ(L) form a fractal invariant triple, a manifestation<br>of a single principle of scale-invariant structural stability.<br>Keywords: Deformed GUE Kernel, Riemann Zeta Spectrum, McKean-Vlasov, Topos The<br>ory, Fractal Coherence, Structural Stability.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17967456 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Structural Isomorphisms between Deformed GUE Kernels, Fractal Fokker-Planck Dynamics, and Open Logical Systems Gutiérrez, Marco Llere Riemann zeta zeros Random Matrix Theory Determinantal Point Processes McKean–Vlasov dynamics Mathematical PhysicsFractal coherence <p>Theoretical physics currently faces a disjointed landscape regarding the modeling of com<br>plex stability: Random Matrix Theory (RMT) assumes universal GUE statistics, stochastic<br>dynamics rely on standard Fokker-Planck evolution, and formal logic grapples with incom<br>pleteness in closed systems. In this work, I present evidence that these three domains share<br>a common, underlying geometric constraint structure: multiscale fractal coherence.<br>First, based on a high-precision spectral analysis (N = 105 Riemann zeros), I report a<br>systematic determinantal asymmetry (∆β ≈ 0.217) that converges asymptotically, suggest<br>ing a structural rigidity not contemplated in the pure GUE model. I model this anomaly via<br>an additive deformation of the sine kernel, induced by a background arithmetic structure.<br>Second, I establish an isomorphism between this deformation and the steady state of<br>a McKean-Vlasov equation with long-range interaction. I show that the dynamic contain<br>ment term acts by penalizing fine fluctuations, generating increasing rigidity in the system<br>analogous to spectral viscosity.<br>Third, I formalize the conservation of this structure using Topos Theory, defining the<br>aperture operator L as a functor that preserves functional coherence Φ across a hierarchy<br>of systems.<br>I propose that the spectral deformation parameter γ, the dynamic containment coefficient<br>λ, and the logical aperture degree κ(L) form a fractal invariant triple, a manifestation<br>of a single principle of scale-invariant structural stability.<br>Keywords: Deformed GUE Kernel, Riemann Zeta Spectrum, McKean-Vlasov, Topos The<br>ory, Fractal Coherence, Structural Stability.</p> |
| title | Structural Isomorphisms between Deformed GUE Kernels, Fractal Fokker-Planck Dynamics, and Open Logical Systems |
| topic | Riemann zeta zeros Random Matrix Theory Determinantal Point Processes McKean–Vlasov dynamics Mathematical PhysicsFractal coherence |
| url | https://doi.org/10.5281/zenodo.17967456 |