We introduce the EDEN kernel $\Psi: \mathbb{R}^+ \to \mathbb{R}$, a discriminator functional derived from the Jacobi theta function and its functional equation. The kernel achieves optimal separation between signal and noise components in spectral decompositions, attaining its global minimum at $x = 1$ with $\Psi(1) \approx -0.543$. We provide the complete mathematical derivation, prove essential properties, establish the connection to heat diffusion and modular forms, and demonstrate 100\% discrimination accuracy for signal-to-noise ratios $\geq 1$. The kernel respects the Landauer thermodynamic limit, returning null when signals have dissolved below SNR $\approx 0.5$. Full computational algorithms are provided.