This document outlines a proof that the Hodge Conjecture, demonstrated through methods involving Riemannian geometry and spectral analysis, necessarily implies the full set of Grothendieck's Standard Conjectures in algebraic geometry. The cornerstone of the argument is that the Hodge Conjecture is equivalent to establishing Standard Conjecture C, which posits that the intersection form on primitive cohomology is positive definite. The proof of this initial implication relies on the spectral analysis of a Hermitian operator, termed the "Algebraic Discriminator," which connects the algebraic nature of Hodge classes to the positive semi-definiteness of the operator. Once Standard Conjecture C is established, the remaining conjectures (D, A, and B) follow through a known, albeit profound, logical cascade.