Zeta Riemann Encoding Conjecture

We propose a framework inspired by the Hilbert--Pólya conjecture that directly links the ground state of a radial Schrödinger operator to the analytic structure of the Riemann zeta function. We define a self-adjoint operator on L²(R₊,ydy) with potential V(y) that is smooth, confining, and self-dual. We propose the " Zeta Riemann Encoding Conjecture" (ZREC), that is Mellin transform of the normalized ground state wave function M[ψ₀] is equal to the completed zeta function ξ(s). We find an interesting result, that the symmetry ψ₀(y)=(1/y)ψ₀((1/y)) imposes on its Mellin transform, Φ(s), a functional equation that is exactly analogous to the one for the completed Riemann zeta function ξ(s). A concrete V(y) built from the von Mangoldt function Λ(n) is numerically optimized. Although the potential used does not fully satisfy all theoretical requirements, it accurately reproduces the first 60 nontrivial Riemann zeros, providing strong numerical evidence for the ZREC. .