A Zero-Less Regularized Sum for the Riemann Zeta Function with n⁴ Cutoff: Computational Framework and Mellin Correction

We introduce a null-state regularization Phi_X(s) = sum(n^-s / (1 + n^4/X^4)) inspired by Ramanujan's denominator. We separate trivial zeros (s = -2k, divergence to All-state A) from non-trivial zeros (Null-state ∅). We prove the balance lemma where the conjugation of B(s) equals B(s) if and only if Re(s) = 1/2. We formulate Lemma 0 via the Mellin transform, showing Phi_X(s) approaches the Zeta function plus the leading pole X¹⁻ˢ. Numerically, we demonstrate that the full Ramanujan correction achieves the expected O(X^-4) decay at non-trivial zeros. We state a consistency conjecture equivalent to the Riemann Hypothesis as open. This is not a proof of RH.