On the Formulation of the Stratum Equation: A Discrete Analog of GR in the Unified Wave Cosmological Model
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2026
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| _version_ | 1866901876668104704 |
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| author | Slavutskiy, Gleb |
| author_facet | Slavutskiy, Gleb |
| contents | <p>Abstract<br>Within the framework of the Unified Wave Cosmological Model (UWCM), spacetime (the<br>Stratum) is a discrete quantized network with a minimal scale—the Planck length lP. In works<br>[1–4], the following results were obtained:<br>• mass quantization: M = N ·mP, N ∈ N;<br>• energy transfer quantization: ∆E = k · EP;<br>• information quantization (holographic principle);<br>• time quantization: ∆t = n· tP;<br>• resolution of quantum paradoxes via discrete dynamics.<br>However, the key element of UWCM formalization—a discrete analog of Einstein’s equation<br>(the Stratum equation)—has not yet been obtained in closed form.<br>The present work is a problem statement for the Stratum equation. Principles that it must<br>satisfy are formulated: discreteness, quantization of the gravitational radius (Rs = 2NlP),<br>elimination of singularities, and the correspondence principle with GR. A qualitative sketch of<br>a possible form of the equation is proposed, based on the discretization of the Laplacian. Open<br>questions are listed explicitly.<br>The work concludes with an invitation to collaboration: the task of formalizing the Stratum<br>equation requires the collective efforts of mathematicians and physicists and cannot be solved<br>alone.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19518993 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | On the Formulation of the Stratum Equation: A Discrete Analog of GR in the Unified Wave Cosmological Model Slavutskiy, Gleb Keywords: quantum gravity, loop quantum gravity, LQG, string theory, discrete space time, Planck length, Planck time, mass quantization, time quantization, holographic principle, AdS/CFT correspondence, Einstein equation, GR, general relativity, Regge calculus, causal dynamical triangulation, CDT, singularity, black holes, dark matter, dark energy, measure ment problem, quantum paradoxes, Schr¨odinger's cat, wave function collapse, UWCM, Unified Wave Cosmological Model, Stratum equation, SGW, Stratum, Infill, problem statement, open problem, invitation to collaboration. Ключевые слова: квантовая гравитация, петлевая квантовая гравитация, LQG, теория струн, дискретное пространство-время, планковская длина, планковское время, квантование массы, квантование времени, голографический принцип, AdS/CFT соответствие, уравнение Эйнштейна, ОТО,общаятеорияотносительности, Reggecalculus, причинная динамическая триангуляция, CDT, сингулярность, чёрные дыры, тёмная материя, тёмная энергия, проблема измерения, квантовые парадоксы, кот Шрёдингера, коллапс волновой функции, ЕВКМ, Единая Волновая Космологическая Модель, уравнение Пласта, СГВ, Пласт, Наполнение, постановка задачи, открытая проблема, приглашение к сотрудничеству <p>Abstract<br>Within the framework of the Unified Wave Cosmological Model (UWCM), spacetime (the<br>Stratum) is a discrete quantized network with a minimal scale—the Planck length lP. In works<br>[1–4], the following results were obtained:<br>• mass quantization: M = N ·mP, N ∈ N;<br>• energy transfer quantization: ∆E = k · EP;<br>• information quantization (holographic principle);<br>• time quantization: ∆t = n· tP;<br>• resolution of quantum paradoxes via discrete dynamics.<br>However, the key element of UWCM formalization—a discrete analog of Einstein’s equation<br>(the Stratum equation)—has not yet been obtained in closed form.<br>The present work is a problem statement for the Stratum equation. Principles that it must<br>satisfy are formulated: discreteness, quantization of the gravitational radius (Rs = 2NlP),<br>elimination of singularities, and the correspondence principle with GR. A qualitative sketch of<br>a possible form of the equation is proposed, based on the discretization of the Laplacian. Open<br>questions are listed explicitly.<br>The work concludes with an invitation to collaboration: the task of formalizing the Stratum<br>equation requires the collective efforts of mathematicians and physicists and cannot be solved<br>alone.</p> |
| title | On the Formulation of the Stratum Equation: A Discrete Analog of GR in the Unified Wave Cosmological Model |
| topic | Keywords: quantum gravity, loop quantum gravity, LQG, string theory, discrete space time, Planck length, Planck time, mass quantization, time quantization, holographic principle, AdS/CFT correspondence, Einstein equation, GR, general relativity, Regge calculus, causal dynamical triangulation, CDT, singularity, black holes, dark matter, dark energy, measure ment problem, quantum paradoxes, Schr¨odinger's cat, wave function collapse, UWCM, Unified Wave Cosmological Model, Stratum equation, SGW, Stratum, Infill, problem statement, open problem, invitation to collaboration. Ключевые слова: квантовая гравитация, петлевая квантовая гравитация, LQG, теория струн, дискретное пространство-время, планковская длина, планковское время, квантование массы, квантование времени, голографический принцип, AdS/CFT соответствие, уравнение Эйнштейна, ОТО,общаятеорияотносительности, Reggecalculus, причинная динамическая триангуляция, CDT, сингулярность, чёрные дыры, тёмная материя, тёмная энергия, проблема измерения, квантовые парадоксы, кот Шрёдингера, коллапс волновой функции, ЕВКМ, Единая Волновая Космологическая Модель, уравнение Пласта, СГВ, Пласт, Наполнение, постановка задачи, открытая проблема, приглашение к сотрудничеству |
| url | https://doi.org/10.5281/zenodo.19518993 |