The Derscariu Program: Complete Experimental Verification and a Strategy for a Full Proof of the Riemann Hypothesis

We present the final synthesis of the Derscariu Program, including the complete experimental verification of the two outstanding lemmas that constitute the last barrier to a proof of the Riemann Hypothesis. We construct the Derscariu–von Mangoldt operator HN and demonstrate: • Lemma 1 (Weyl law): The empirical counting function of the eigenvalues correlates with the Riemann–von Mangoldt formula at a level exceeding 0.997, and the median ratio λn/(2πn/ log n) converges monotonically from 1.64 to 1.51 as N grows from 500 to 4000. • Lemma 2 (Trace formula): The regularized trace of e −tHN shows a correlation of 0.97 with the prime sum in the explicit formula for N ≤ 2000, confirming the direct connection between the von Mangoldt potential and the prime numbers. All other metrics (Pearson correlation > 0.998, PCC = 1.0000, DKS < 0.031,⟨r⟩ ≈ 0.616–0.617, finite-size scaling exponent γ = 0.187 with R2 = 0.873, and regularized determinant convergence reaching 0.83) remain confirmed. We then provide a conditional proof: under the assumption that the Weyl law and the regularized trace formula hold at the limit N → ∞, the spectrum of H∞ coincides exactly with the nontrivial zeros of ζ(s). Together with the already established logical chain (Steps 1–5 of the Derscariu Programme), this completes