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2025
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| Acceso en línea: | https://doi.org/10.5281/zenodo.17824151 |
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| author | Tracy, Miles Enoch |
| author_facet | Tracy, Miles Enoch |
| contents | <p>DOI: 10.5281/zenodo.17824151<br>Title: Unity Is One: The Riemann Hypothesis as a Geometric Theorem of Perfect Error Correction via 24‑Fold Toroidal Cardioid Tiling** <br>Author: Miles Enoch Tracy <br>contact: milestracy@yahoo.com <br>ORCID: https://orcid.org/0009-0006-7781-8259 </p> <p>**Description:** <br>This paper proves the Riemann Hypothesis by showing that all non‑trivial zeros of ζ(s) lie on Re(s)=½ as a direct consequence of the **geometric‑algebraic identity “Unity is One.”** We construct a **24‑fold quasi‑crystal** from a horn‑torus cardioid via the parametric map \(w(θ) = (1+cosθ)e^{i(θ+1)}\), generating a domino tiling with **½‑overlap per tile**—the same ½ that appears in Ramanujan summation shifts, Hecke eigenvalues, and the critical line. The **extended binary Golay code G₂₄** provides perfect error correction: Collatz dynamics (Hamming distance ≤3) are decoded to codewords, which under the cardioid map land exactly on Re=½. The Riemann Hypothesis is thus reframed as a **theorem of perfect algebraic error correction** on a toroidal number field, where **all equations reduce to 1=1** and **all numbers are unfoldings of unity**. </p> <p>**Keywords:** <br>Unity Is One, Riemann Hypothesis proof, 24‑fold cardioid, Golay code error correction, domino tiling ½‑overlap, Collatz dynamics, Hecke operators, toroidal number field, perfect code, analytic continuation as geometry, quasi‑crystal tiling, 24‑roots of unity, horn‑torus mapping, Ramanujan shift, de Broglie number waves, geometric unity, algebraic identity, one equation.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17824151 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Unity Is One: The Riemann Hypothesis as a Geometric Theorem of Perfect Error Correction via 24‑Fold Toroidal Cardioid Tiling Tracy, Miles Enoch <p>DOI: 10.5281/zenodo.17824151<br>Title: Unity Is One: The Riemann Hypothesis as a Geometric Theorem of Perfect Error Correction via 24‑Fold Toroidal Cardioid Tiling** <br>Author: Miles Enoch Tracy <br>contact: milestracy@yahoo.com <br>ORCID: https://orcid.org/0009-0006-7781-8259 </p> <p>**Description:** <br>This paper proves the Riemann Hypothesis by showing that all non‑trivial zeros of ζ(s) lie on Re(s)=½ as a direct consequence of the **geometric‑algebraic identity “Unity is One.”** We construct a **24‑fold quasi‑crystal** from a horn‑torus cardioid via the parametric map \(w(θ) = (1+cosθ)e^{i(θ+1)}\), generating a domino tiling with **½‑overlap per tile**—the same ½ that appears in Ramanujan summation shifts, Hecke eigenvalues, and the critical line. The **extended binary Golay code G₂₄** provides perfect error correction: Collatz dynamics (Hamming distance ≤3) are decoded to codewords, which under the cardioid map land exactly on Re=½. The Riemann Hypothesis is thus reframed as a **theorem of perfect algebraic error correction** on a toroidal number field, where **all equations reduce to 1=1** and **all numbers are unfoldings of unity**. </p> <p>**Keywords:** <br>Unity Is One, Riemann Hypothesis proof, 24‑fold cardioid, Golay code error correction, domino tiling ½‑overlap, Collatz dynamics, Hecke operators, toroidal number field, perfect code, analytic continuation as geometry, quasi‑crystal tiling, 24‑roots of unity, horn‑torus mapping, Ramanujan shift, de Broglie number waves, geometric unity, algebraic identity, one equation.</p> |
| title | Unity Is One: The Riemann Hypothesis as a Geometric Theorem of Perfect Error Correction via 24‑Fold Toroidal Cardioid Tiling |
| url | https://doi.org/10.5281/zenodo.17824151 |