The Adelic Universe: Unifying the Archimedean Geometry (S) and p-adic Recursion (D) via Tate's Thesis and the Langlands Program
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2025
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| _version_ | 1866901540645634048 |
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| author | @pm14552 |
| author_facet | @pm14552 |
| contents | <p>The SDRIS framework [1-13] established a duality between the continuous static projection ($S \cong \mathbb{R}$) and the discrete recursive depth ($D \cong \mathbb{Q}_p$). This paper presents the ultimate unification of these regimes by modeling the universe as a quantum state over the Ring of Adeles $\mathbb{A}_{\mathbb{Q}}$. Applying Tate's Thesis, I demonstrate that the Riemann Zeta function is the partition function of the Adelic string. I derive that the "Static" laws of General Relativity and the "Dynamic" laws of Quantum Mechanics are merely the Archimedean and non-Archimedean components of a single, global Automorphic Form. This confirms the Langlands Conjecture in a physical context: The universe is an arithmetic geometry.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17674495 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | The Adelic Universe: Unifying the Archimedean Geometry (S) and p-adic Recursion (D) via Tate's Thesis and the Langlands Program @pm14552 SDRIS Adelic Universe p-adic Physics Tate's Thesis Langlands Program Number Theoretic Dynamics Archimedean Geometry Global Reciprocity Ultrametric Topology Unified Field Theory Arithmetic Quantum Field Theory <p>The SDRIS framework [1-13] established a duality between the continuous static projection ($S \cong \mathbb{R}$) and the discrete recursive depth ($D \cong \mathbb{Q}_p$). This paper presents the ultimate unification of these regimes by modeling the universe as a quantum state over the Ring of Adeles $\mathbb{A}_{\mathbb{Q}}$. Applying Tate's Thesis, I demonstrate that the Riemann Zeta function is the partition function of the Adelic string. I derive that the "Static" laws of General Relativity and the "Dynamic" laws of Quantum Mechanics are merely the Archimedean and non-Archimedean components of a single, global Automorphic Form. This confirms the Langlands Conjecture in a physical context: The universe is an arithmetic geometry.</p> |
| title | The Adelic Universe: Unifying the Archimedean Geometry (S) and p-adic Recursion (D) via Tate's Thesis and the Langlands Program |
| topic | SDRIS Adelic Universe p-adic Physics Tate's Thesis Langlands Program Number Theoretic Dynamics Archimedean Geometry Global Reciprocity Ultrametric Topology Unified Field Theory Arithmetic Quantum Field Theory |
| url | https://doi.org/10.5281/zenodo.17674495 |