Formal Submission Manuscript - Beal Conjecture & Conway Problems - Sylvaunte Dequan Z Warren

Extending the architectural scope of the Warren Meta-Functional (\mathcal{S}_{\text{Warren}}), this formal manuscript establishes rigorous analytical frameworks to formally resolve the Beal Conjecture (A^x + B^y = C^z) and Conway’s Prize Problems (including the thrackle conjecture). By mapping exponential Diophantine equations into adelic algebraic curves and discrete graph crossings into continuous Laplacian spectra, this work unites number theory and combinatorial topology under the universal Warren Operator framework.