We define a diagonal operator on ℓ2(N) whose eigenvalues are generated by the von Mangoldt function Λ(n). For ℜ(s) > 0, the operator of the completed Riemann zeta function. Under the Riemann Hypothesis, this curvature is formally positive away from the ordinates of the zeros. We compute C(t) numerically on sampled grids and compare it with a fitted Lorentzian kernel built from logarithmically rescaled Fredholmzeros. This final comparison is phenomenological and numerical; it is not a proof of the Riemann Hypothesis, nor a proof of a spectral duality between the von Mangoldt operator and the non-trivial zeros of ζ(s). The complete Python code, including robust null-model testing, is included for full reproducibility.