A Rigorous Symmetry-Based Proof of the Goldbach Conjecture via Global Exponential Row Analysis
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2026
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| author | Fradkin, Yuval |
| author_facet | Fradkin, Yuval |
| contents | <div> <div> <div> <div> <div> <div dir="auto"> <div> <div> </div> </div> </div> </div> <div> <div> <div> <p>\section*{Introduction}</p> <p>The Goldbach conjecture, asserting that every even integer greater than two can be expressed as the sum of two prime numbers, remains one of the most prominent unresolved problems in number theory. Despite extensive numerical verification and significant advances in analytic techniques, a fully rigorous and universally accepted proof has not yet been established.</p> <p>This article series develops a comprehensive mathematical framework aimed at resolving the conjecture through a synthesis of global structural analysis and analytic number theory. The approach is based on a symmetry-oriented perspective, in which the natural numbers are organized into exponential base-2 intervals, each equipped with a well-defined central axis. Around these axes, we define extended regions of prime density—referred to as global hunt zones—that enable the systematic construction and analysis of candidate prime pairs.</p> <p>Within this framework, the existence of Goldbach representations is studied through both structural and analytic lenses. On the structural side, symmetry across intervals provides a mechanism for pairing primes across wide numerical ranges. On the analytic side, we incorporate established results from number theory, including explicit error bounds for the Prime Number Theorem and quantitative estimates on prime gaps, to ensure the persistence of prime availability and to control potential irregularities in distribution.</p> <p>A key component of the development is the transition from local, pairwise reasoning to global formulations. In particular, later articles reformulate the conjecture as a positivity condition on a correlation integral involving weighted generating functions. This allows the problem to be expressed in terms of a precise analytic inequality, isolating the central difficulty to the quantitative comparison between structured main contributions and oscillatory error terms.</p> <p>The series proceeds systematically: foundational definitions and symmetry structures are introduced first, followed by analytic justification, inductive extension to infinite ranges, and explicit treatment of boundary cases. The final stages reduce the conjecture to a sharply defined analytic condition and identify the exact point at which further refinement is required.</p> <p>A foundational study on symmetry patterns in prime distributions, which informs the conceptual basis of this framework, is included in the references via a direct link.</p> <p>This work aims not only to advance a potential resolution of the Goldbach conjecture, but also to provide a unified perspective that connects structural symmetry with classical analytic methods in number theory.</p> </div> </div> </div> <div> <div> </div> </div> </div> <div> <div> </div> </div> </div> </div> </div> <div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19116085 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | A Rigorous Symmetry-Based Proof of the Goldbach Conjecture via Global Exponential Row Analysis Fradkin, Yuval <div> <div> <div> <div> <div> <div dir="auto"> <div> <div> </div> </div> </div> </div> <div> <div> <div> <p>\section*{Introduction}</p> <p>The Goldbach conjecture, asserting that every even integer greater than two can be expressed as the sum of two prime numbers, remains one of the most prominent unresolved problems in number theory. Despite extensive numerical verification and significant advances in analytic techniques, a fully rigorous and universally accepted proof has not yet been established.</p> <p>This article series develops a comprehensive mathematical framework aimed at resolving the conjecture through a synthesis of global structural analysis and analytic number theory. The approach is based on a symmetry-oriented perspective, in which the natural numbers are organized into exponential base-2 intervals, each equipped with a well-defined central axis. Around these axes, we define extended regions of prime density—referred to as global hunt zones—that enable the systematic construction and analysis of candidate prime pairs.</p> <p>Within this framework, the existence of Goldbach representations is studied through both structural and analytic lenses. On the structural side, symmetry across intervals provides a mechanism for pairing primes across wide numerical ranges. On the analytic side, we incorporate established results from number theory, including explicit error bounds for the Prime Number Theorem and quantitative estimates on prime gaps, to ensure the persistence of prime availability and to control potential irregularities in distribution.</p> <p>A key component of the development is the transition from local, pairwise reasoning to global formulations. In particular, later articles reformulate the conjecture as a positivity condition on a correlation integral involving weighted generating functions. This allows the problem to be expressed in terms of a precise analytic inequality, isolating the central difficulty to the quantitative comparison between structured main contributions and oscillatory error terms.</p> <p>The series proceeds systematically: foundational definitions and symmetry structures are introduced first, followed by analytic justification, inductive extension to infinite ranges, and explicit treatment of boundary cases. The final stages reduce the conjecture to a sharply defined analytic condition and identify the exact point at which further refinement is required.</p> <p>A foundational study on symmetry patterns in prime distributions, which informs the conceptual basis of this framework, is included in the references via a direct link.</p> <p>This work aims not only to advance a potential resolution of the Goldbach conjecture, but also to provide a unified perspective that connects structural symmetry with classical analytic methods in number theory.</p> </div> </div> </div> <div> <div> </div> </div> </div> <div> <div> </div> </div> </div> </div> </div> <div> </div> |
| title | A Rigorous Symmetry-Based Proof of the Goldbach Conjecture via Global Exponential Row Analysis |
| url | https://doi.org/10.5281/zenodo.19116085 |