The Sobolev-Ozok Lattice K-Cycle Law, Space Evolution, Coherence Invariants, and the Cosmological Reset Mechanism
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| Format: | Recurso digital |
| Language: | English |
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2025
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| _version_ | 1866901679011528704 |
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| author | Ozok, Ozcan |
| author_facet | Ozok, Ozcan |
| contents | <p>This paper develops a fully self-contained cosmological framework based on the Sobolev–Ozok Lattice (SOL), in which space, time, matter, and gravitational curvature emerge from discrete coherence interactions between Planck-scale units. The central result is the K-Cycle Law, a recursive refinement mechanism acting across Sobolev orders K=0→6, which governs the evolution, dimensionality, stability, and thermodynamic behavior of the Universe.</p> <p>A major outcome of this work is the discovery that the Cosmic Microwave Background (CMB) temperature arises naturally from the K-cycle recursion. Without invoking inflation, dark energy, or external scaling assumptions, the model produces a numerical prediction</p> <p>TCMB≈2.727 K</p> <p>in striking agreement with COBE, WMAP, and Planck observations. This value emerges directly from the structural properties of the SOL recursion, the decoherence entropy functional, and the asymptotic behavior of the K=1 coherence surface.</p> <p>The paper also demonstrates how gravitational curvature, electromagnetic propagation, cosmic expansion, matter formation, and black-hole thresholds are unified under a single expression of coherence tension, which replaces the classical field paradigm with a purely geometric–informational structure. The cosmological “reset mechanism,” corresponding to the K=6 collapse boundary, provides a cyclic origin for universes and a natural explanation for global homogenization.</p> <p>Extensive appendices provide formal derivations of the recursive K-cycle law, the emergent metric structure, the decoherence spectral distribution, the cosmological scale factor, the universal tension functional, and the asymptotic fractal structure of the coherence-decoherence interface. The model numerically reconstructs the present-day Universe radius, horizon fraction, and thermal spectrum using only Planck-scale constants and the internal symmetry of the SOL recursion.</p> <p>This work forms a key part of the growing SOL research program, aimed at unifying general relativity, quantum behavior, black-hole physics, thermodynamics, and cosmology through coherence-based discretization.</p> <div dir="auto"><strong>Decleration of Tools Used:</strong></div> <div dir="auto">This paper was prepared and formatted using Overleaf (LaTeX editor). Text refinement and language polishing were assisted by Overleaf AI Editor. all scientific content, derivations, and conclusions are original and autored by the undersigned.</div> <div dir="auto"> <p>This paper is part of the Sobolev–Ozok Lattice (SOL) research program.</p> <p><strong>Project webpage (papers, figures, updates):</strong></p> <p><a href="https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/" target="_blank" rel="noopener">https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/</a></p> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17754278 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Sobolev-Ozok Lattice K-Cycle Law, Space Evolution, Coherence Invariants, and the Cosmological Reset Mechanism Ozok, Ozcan Sobolev–Ozok Lattice (SOL) K-cycle recursion Planck-scale cosmology Coherence–decoherence dynamics Emergent spacetime Coherence tension Recursive universe model Pre-geometric physics Coherence invariants Cosmological reset mechanism Cosmic Microwave Background (CMB) CMB temperature derivation Cosmological expansion Horizon problem Universe age and radius Blackbody radiation Cosmological structure formation Emergent gravity Gravitational curvature Metric emergence Black hole thresholds Void black holes Quasi-black-hole structures Coherence-based gravity Sobolev norms Functional analysis Coherence gradients Discrete lattice model Harmonic analysis Recursive refinement Nonlinear scaling laws Planck-scale resolution K=0 to K=6 transition Coherence hierarchy Decoherence entropy High-order coherence (K>4) Quaternion coherence <p>This paper develops a fully self-contained cosmological framework based on the Sobolev–Ozok Lattice (SOL), in which space, time, matter, and gravitational curvature emerge from discrete coherence interactions between Planck-scale units. The central result is the K-Cycle Law, a recursive refinement mechanism acting across Sobolev orders K=0→6, which governs the evolution, dimensionality, stability, and thermodynamic behavior of the Universe.</p> <p>A major outcome of this work is the discovery that the Cosmic Microwave Background (CMB) temperature arises naturally from the K-cycle recursion. Without invoking inflation, dark energy, or external scaling assumptions, the model produces a numerical prediction</p> <p>TCMB≈2.727 K</p> <p>in striking agreement with COBE, WMAP, and Planck observations. This value emerges directly from the structural properties of the SOL recursion, the decoherence entropy functional, and the asymptotic behavior of the K=1 coherence surface.</p> <p>The paper also demonstrates how gravitational curvature, electromagnetic propagation, cosmic expansion, matter formation, and black-hole thresholds are unified under a single expression of coherence tension, which replaces the classical field paradigm with a purely geometric–informational structure. The cosmological “reset mechanism,” corresponding to the K=6 collapse boundary, provides a cyclic origin for universes and a natural explanation for global homogenization.</p> <p>Extensive appendices provide formal derivations of the recursive K-cycle law, the emergent metric structure, the decoherence spectral distribution, the cosmological scale factor, the universal tension functional, and the asymptotic fractal structure of the coherence-decoherence interface. The model numerically reconstructs the present-day Universe radius, horizon fraction, and thermal spectrum using only Planck-scale constants and the internal symmetry of the SOL recursion.</p> <p>This work forms a key part of the growing SOL research program, aimed at unifying general relativity, quantum behavior, black-hole physics, thermodynamics, and cosmology through coherence-based discretization.</p> <div dir="auto"><strong>Decleration of Tools Used:</strong></div> <div dir="auto">This paper was prepared and formatted using Overleaf (LaTeX editor). Text refinement and language polishing were assisted by Overleaf AI Editor. all scientific content, derivations, and conclusions are original and autored by the undersigned.</div> <div dir="auto"> <p>This paper is part of the Sobolev–Ozok Lattice (SOL) research program.</p> <p><strong>Project webpage (papers, figures, updates):</strong></p> <p><a href="https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/" target="_blank" rel="noopener">https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/</a></p> </div> |
| title | The Sobolev-Ozok Lattice K-Cycle Law, Space Evolution, Coherence Invariants, and the Cosmological Reset Mechanism |
| topic | Sobolev–Ozok Lattice (SOL) K-cycle recursion Planck-scale cosmology Coherence–decoherence dynamics Emergent spacetime Coherence tension Recursive universe model Pre-geometric physics Coherence invariants Cosmological reset mechanism Cosmic Microwave Background (CMB) CMB temperature derivation Cosmological expansion Horizon problem Universe age and radius Blackbody radiation Cosmological structure formation Emergent gravity Gravitational curvature Metric emergence Black hole thresholds Void black holes Quasi-black-hole structures Coherence-based gravity Sobolev norms Functional analysis Coherence gradients Discrete lattice model Harmonic analysis Recursive refinement Nonlinear scaling laws Planck-scale resolution K=0 to K=6 transition Coherence hierarchy Decoherence entropy High-order coherence (K>4) Quaternion coherence |
| url | https://doi.org/10.5281/zenodo.17754278 |