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Zenodo
2026
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| Truy cập trực tuyến: | https://doi.org/10.5281/zenodo.19765735 |
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| _version_ | 1866901144152834048 |
|---|---|
| author | Moorehead-McDaniel, Stephen |
| author_facet | Moorehead-McDaniel, Stephen |
| contents | <p>This paper addresses the historical incompatibility between General Relativity and Quantum Mechanics by dismantling the traditional assumption of a continuous spacetime manifold. Instead, it proposes that the physical vacuum is an absolutely discrete, rigidly quantized H4 simplicial quasicrystal. To bridge the gap between this microscopic quantum lattice and the continuous macroscopic world, the paper introduces the mathematical protocol of Spectral Decimation. This technique maps the high-frequency topological microstates of the vacuum to low-frequency macroscopic observables, completely bypassing the pathological, infinitely small dimensional limits required by orthodox calculus. </p> <p>By replacing continuous wave operators with a discrete graph Laplacian, the spatial domain is rigidly bounded, enforcing a strict maximum topological frequency. This structural limit guarantees that the infinite-energy modes responsible for gravitational singularities physically cannot exist. Through the decimation process, the continuous metric tensor and the Einstein Field Equations are formally revealed to be emergent properties, representing the low-energy elastodynamic equilibrium of the underlying lattice. </p> <p>Furthermore, this geometric framework abandons the search for an elementary graviton particle propagating through a continuous background. Instead, the graviton emerges mathematically as a low-frequency acoustic phonon—a structural vibration—of the H4 quasicrystal. Gravity is therefore redefined strictly as the solid-state mechanics of the quantized void. Ultimately, this model deterministically resolves the ultraviolet catastrophes of quantum gravity, mathematically erasing infinity and realizing Albert Einstein's pursuit of a Unified Field Theory bounded by pure geometry. </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19765735 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Discrete Geometric Foundations Moorehead-McDaniel, Stephen <p>This paper addresses the historical incompatibility between General Relativity and Quantum Mechanics by dismantling the traditional assumption of a continuous spacetime manifold. Instead, it proposes that the physical vacuum is an absolutely discrete, rigidly quantized H4 simplicial quasicrystal. To bridge the gap between this microscopic quantum lattice and the continuous macroscopic world, the paper introduces the mathematical protocol of Spectral Decimation. This technique maps the high-frequency topological microstates of the vacuum to low-frequency macroscopic observables, completely bypassing the pathological, infinitely small dimensional limits required by orthodox calculus. </p> <p>By replacing continuous wave operators with a discrete graph Laplacian, the spatial domain is rigidly bounded, enforcing a strict maximum topological frequency. This structural limit guarantees that the infinite-energy modes responsible for gravitational singularities physically cannot exist. Through the decimation process, the continuous metric tensor and the Einstein Field Equations are formally revealed to be emergent properties, representing the low-energy elastodynamic equilibrium of the underlying lattice. </p> <p>Furthermore, this geometric framework abandons the search for an elementary graviton particle propagating through a continuous background. Instead, the graviton emerges mathematically as a low-frequency acoustic phonon—a structural vibration—of the H4 quasicrystal. Gravity is therefore redefined strictly as the solid-state mechanics of the quantized void. Ultimately, this model deterministically resolves the ultraviolet catastrophes of quantum gravity, mathematically erasing infinity and realizing Albert Einstein's pursuit of a Unified Field Theory bounded by pure geometry. </p> |
| title | Discrete Geometric Foundations |
| url | https://doi.org/10.5281/zenodo.19765735 |