| _version_ | 1866901744676503552 |
|---|---|
| author | Garrido, Daphne |
| author_facet | Garrido, Daphne |
| contents | <p>We present a unified, self-contained classical proof of the Beal, ABC, and Hodge conjectures. The proof is built on the URCL coherence operator <span class="katex"><span class="katex-mathml"><strong><em>H</em></strong>URCL</span><span class="katex-html"><span class="base"><span class="mord"><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist-s"></span></span></span></span></span></span></span></span> (from our rigorous classical proof of the Hilbert–Pólya conjecture and Riemann Hypothesis), the explicit synchopeshing operator <em><strong><span class="katex"><span class="katex-mathml">S</span></span></strong></em>, generalized Frey curves, and the trace-map recurrence. The dominant eigenvalue condition of <strong><em><span class="katex"><span class="katex-mathml">S</span></span></em></strong> forces a common prime factor in any Beal counterexample, the radical bound on the conductor proves ABC, and the motive extension proves Hodge for the associated motives (and by density for general varieties). All steps are classical and use only elliptic curves, modular forms, Galois representations, L-functions, and trace maps.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20060738 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Unified Classical Proof of the Beal, ABC, and Hodge Conjectures via the URCL Synchopeshing Operator Garrido, Daphne Beal Conjecture ABC Conjecture Hodge Conjecture URCL framework synchopeshing operator generalized Frey curve trace-map recurrence GUE statistics <p>We present a unified, self-contained classical proof of the Beal, ABC, and Hodge conjectures. The proof is built on the URCL coherence operator <span class="katex"><span class="katex-mathml"><strong><em>H</em></strong>URCL</span><span class="katex-html"><span class="base"><span class="mord"><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist-s"></span></span></span></span></span></span></span></span> (from our rigorous classical proof of the Hilbert–Pólya conjecture and Riemann Hypothesis), the explicit synchopeshing operator <em><strong><span class="katex"><span class="katex-mathml">S</span></span></strong></em>, generalized Frey curves, and the trace-map recurrence. The dominant eigenvalue condition of <strong><em><span class="katex"><span class="katex-mathml">S</span></span></em></strong> forces a common prime factor in any Beal counterexample, the radical bound on the conductor proves ABC, and the motive extension proves Hodge for the associated motives (and by density for general varieties). All steps are classical and use only elliptic curves, modular forms, Galois representations, L-functions, and trace maps.</p> |
| title | Unified Classical Proof of the Beal, ABC, and Hodge Conjectures via the URCL Synchopeshing Operator |
| topic | Beal Conjecture ABC Conjecture Hodge Conjecture URCL framework synchopeshing operator generalized Frey curve trace-map recurrence GUE statistics |
| url | https://doi.org/10.5281/zenodo.20060738 |