A Topological Geometrodynamics of Wave Functions: \break On the Stationary State Wave Functions, Their Partial Time Derivative and Resultant Theoretical Implications Book VII: The Topological Geometrodynamics - The Geometry of Travel and Use Cases II
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2026
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| author | Parashkevov, Emil |
| author_facet | Parashkevov, Emil |
| contents | <p>Book VII marks the next evolution step of the Topological Geometrodynamics (<span class="math-inline">$\mathcal{M}^5$</span>) framework, transitioning from foundational differential geometry to applied, deterministic physical mechanics. This volume demonstrates that the seemingly disparate forces of classical astrophysics and quantum field theory are not independent phenomena, but are the unavoidable, exact differential shadows of a single geometric axiom: the quantization of physical action (<span class="math-inline">$p_{_A} x^A = N\hbar$</span>) evaluated across a continuous complex manifold.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> <p> </p> <p>By strictly defining the universe as a 4-dimensional double-cover mapped onto a 1D complex plane (<span class="math-inline">$z = \epsilon + i\gamma$</span>), this volume utilizes a universal mapping limit (the <span class="math-inline">$1/2$</span> geometric trace contraction) to resolve the major anomalies of modern physics without relying on retroactive curve-fitting or perturbation integrals.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> <p> </p> <p><strong>Key Derivations and Unifications:</strong></p> <ul> <li> <p><strong>Scale Invariance of the Trace Contraction:</strong> The framework proves that the exact same algebraic tensor contraction natively outputs both the macroscopic perihelion precession of planets (General Relativity) and the microscopic anomalous magnetic moment of the electron (the Schwinger limit in QED).</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> </li> <li> <p><strong>Gravitational Waves:</strong> The 5.06% mass-energy deficit observed in binary black hole mergers is derived deterministically as the mandatory topological defect of an <span class="math-inline">$S^3$</span> manifold fusion.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> </li> <li> <p><strong>Navier-Stokes Resolution:</strong> The classical fluid singularity is mathematically eradicated, predicting a forced topological phase-transition into a Bose-Einstein Condensate at a strict 31.6 <span class="math-inline">$\mu$</span>m boundary.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> </li> <li> <p><strong>Fractional Quantum Hall Effect:</strong> The exact fractional charge plateaus are derived purely from the spatial fragmentation of a Spin-1/2 Möbius knot.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> </li> </ul> <p><strong>Advanced Theoretical Mechanics & The Illusion of Distance:</strong> Beyond standard unifications, Book VII pushes the <span class="math-inline">$\mathcal{M}^5$</span> geometry to its absolute logical terminus. By proving a topological isomorphism between the black hole core and the macroscopic universe, the framework introduces "Interaction Realism" and the "Entanglement Equivalence Principle". This fundamentally redefines spatial distance as entanglement latency, outlining the theoretical kinematics of macroscopic transit, including "Trans-Shell Tunneling" and "Topological Hijacking" via high-precision proxy states.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> <p> </p> <p><strong>The Epistemology of the Mapping:</strong> To bridge the gap between abstract topology and observable 4D spacetime, the author introduces a vital epistemological framework. The 3-sheeted Riemann surfaces and <span class="math-inline">$6\pi$</span> Cauchy cones utilized herein are presented as the ultimate "analytical compressor." Much like Feynman diagrams or Dirac matrices, the complex plane mapping is utilized as a profound mathematical shortcut—allowing physicists to bypass intractable non-linear tensor calculus and arrive directly at the exact, closed-form algebraic truths of nature.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> <p> </p> <p>The framework is strictly anchored by falsifiable predictions, including a measurable 10-15% reduction in the apparent black hole shadow and a specific anomalous gravitational redshift of <span class="math-inline">$z \approx 1.18$</span> at the black hole transition boundary.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19958894 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Topological Geometrodynamics of Wave Functions: \break On the Stationary State Wave Functions, Their Partial Time Derivative and Resultant Theoretical Implications Book VII: The Topological Geometrodynamics - The Geometry of Travel and Use Cases II Parashkevov, Emil Topological Geometrodynamics General Relativity Quantum Electrodynamics Algebraic Topology Complex Analysis Anomalous Magnetic Moment Fractional Quantum Hall Effect Navier-Stokes Singularity Gravitational Waves Holographic Principle Bose-Einstein Condensate Cauchy Residue Theorem <p>Book VII marks the next evolution step of the Topological Geometrodynamics (<span class="math-inline">$\mathcal{M}^5$</span>) framework, transitioning from foundational differential geometry to applied, deterministic physical mechanics. This volume demonstrates that the seemingly disparate forces of classical astrophysics and quantum field theory are not independent phenomena, but are the unavoidable, exact differential shadows of a single geometric axiom: the quantization of physical action (<span class="math-inline">$p_{_A} x^A = N\hbar$</span>) evaluated across a continuous complex manifold.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> <p> </p> <p>By strictly defining the universe as a 4-dimensional double-cover mapped onto a 1D complex plane (<span class="math-inline">$z = \epsilon + i\gamma$</span>), this volume utilizes a universal mapping limit (the <span class="math-inline">$1/2$</span> geometric trace contraction) to resolve the major anomalies of modern physics without relying on retroactive curve-fitting or perturbation integrals.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> <p> </p> <p><strong>Key Derivations and Unifications:</strong></p> <ul> <li> <p><strong>Scale Invariance of the Trace Contraction:</strong> The framework proves that the exact same algebraic tensor contraction natively outputs both the macroscopic perihelion precession of planets (General Relativity) and the microscopic anomalous magnetic moment of the electron (the Schwinger limit in QED).</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> </li> <li> <p><strong>Gravitational Waves:</strong> The 5.06% mass-energy deficit observed in binary black hole mergers is derived deterministically as the mandatory topological defect of an <span class="math-inline">$S^3$</span> manifold fusion.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> </li> <li> <p><strong>Navier-Stokes Resolution:</strong> The classical fluid singularity is mathematically eradicated, predicting a forced topological phase-transition into a Bose-Einstein Condensate at a strict 31.6 <span class="math-inline">$\mu$</span>m boundary.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> </li> <li> <p><strong>Fractional Quantum Hall Effect:</strong> The exact fractional charge plateaus are derived purely from the spatial fragmentation of a Spin-1/2 Möbius knot.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> </li> </ul> <p><strong>Advanced Theoretical Mechanics & The Illusion of Distance:</strong> Beyond standard unifications, Book VII pushes the <span class="math-inline">$\mathcal{M}^5$</span> geometry to its absolute logical terminus. By proving a topological isomorphism between the black hole core and the macroscopic universe, the framework introduces "Interaction Realism" and the "Entanglement Equivalence Principle". This fundamentally redefines spatial distance as entanglement latency, outlining the theoretical kinematics of macroscopic transit, including "Trans-Shell Tunneling" and "Topological Hijacking" via high-precision proxy states.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> <p> </p> <p><strong>The Epistemology of the Mapping:</strong> To bridge the gap between abstract topology and observable 4D spacetime, the author introduces a vital epistemological framework. The 3-sheeted Riemann surfaces and <span class="math-inline">$6\pi$</span> Cauchy cones utilized herein are presented as the ultimate "analytical compressor." Much like Feynman diagrams or Dirac matrices, the complex plane mapping is utilized as a profound mathematical shortcut—allowing physicists to bypass intractable non-linear tensor calculus and arrive directly at the exact, closed-form algebraic truths of nature.</p> <div class="source-inline-chip-container ng-star-inserted"> </div> <p> </p> <p> </p> <p>The framework is strictly anchored by falsifiable predictions, including a measurable 10-15% reduction in the apparent black hole shadow and a specific anomalous gravitational redshift of <span class="math-inline">$z \approx 1.18$</span> at the black hole transition boundary.</p> |
| title | A Topological Geometrodynamics of Wave Functions: \break On the Stationary State Wave Functions, Their Partial Time Derivative and Resultant Theoretical Implications Book VII: The Topological Geometrodynamics - The Geometry of Travel and Use Cases II |
| topic | Topological Geometrodynamics General Relativity Quantum Electrodynamics Algebraic Topology Complex Analysis Anomalous Magnetic Moment Fractional Quantum Hall Effect Navier-Stokes Singularity Gravitational Waves Holographic Principle Bose-Einstein Condensate Cauchy Residue Theorem |
| url | https://doi.org/10.5281/zenodo.19958894 |