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2026
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| Online Access: | https://doi.org/10.5281/zenodo.20347645 |
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| _version_ | 1866902006888660992 |
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| author | Mourad, Belafsahi |
| author_facet | Mourad, Belafsahi |
| contents | <p>Abstract—This work presents a unique methodology breakthrough in analyzing prime number distribution and the decomposition of highly composite integers. We introduce the "Belfsahi Field", a three-dimensional (3D) topological formalism that confines the apparent anarchy of classical arithmetic within an ordered concave geometric structure called the "Topological Bowl". By applying a strict dimensional reduction through the exclusion of index residues multiples of 3 ({3, 6, 0} mod 9), the field converges toward a pure hexagonal symmetry. The fundamental contribution of this research lies in the discovery of the "Belfsahi Constant" (K_mb ≈ 0.941). Conjugated with a specific curvature tensor, this constant governs the angular inclination of the field's helicoidal trajectories. Numerical simulations deterministically demonstrate that pseudo-prime numbers do not disperse chaotically: they isolate and align along an ascending line of stability (Linear Alignment) on the outer wall of the bowl, parallel to the perfect square nodes. This structural regularity allows for the formulation of a direct geometric factorization algorithm, drastically reducing the computational complexity of standard RSA-type encryption keys.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20347645 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Belfsahi Constant: A New Geometric Approach for Number Factorization via the 3D Topological Field Mourad, Belafsahi <p>Abstract—This work presents a unique methodology breakthrough in analyzing prime number distribution and the decomposition of highly composite integers. We introduce the "Belfsahi Field", a three-dimensional (3D) topological formalism that confines the apparent anarchy of classical arithmetic within an ordered concave geometric structure called the "Topological Bowl". By applying a strict dimensional reduction through the exclusion of index residues multiples of 3 ({3, 6, 0} mod 9), the field converges toward a pure hexagonal symmetry. The fundamental contribution of this research lies in the discovery of the "Belfsahi Constant" (K_mb ≈ 0.941). Conjugated with a specific curvature tensor, this constant governs the angular inclination of the field's helicoidal trajectories. Numerical simulations deterministically demonstrate that pseudo-prime numbers do not disperse chaotically: they isolate and align along an ascending line of stability (Linear Alignment) on the outer wall of the bowl, parallel to the perfect square nodes. This structural regularity allows for the formulation of a direct geometric factorization algorithm, drastically reducing the computational complexity of standard RSA-type encryption keys.</p> <p> </p> |
| title | The Belfsahi Constant: A New Geometric Approach for Number Factorization via the 3D Topological Field |
| url | https://doi.org/10.5281/zenodo.20347645 |