DRCC-WIDTH-ZETA Method (DWZ_V2.1): A Width-Controlled Euler-Maclaurin Reconstruction Method for the Riemann Zeta Function in the Critical Strip

Abstract

We study a controlled, finite approximation of the Riemann zeta function zeta(s) in the critical strip 0 < Re(s) < 1, starting from the DRCC stability condition (DRCC: Dimensional Reduction via Controlled Combinatorics) 0 < d_rec(X) <= d_frag(X) < infinity. The naive partial sum diverges in the critical strip as the truncation width W grows. A first-order Euler-Maclaurin correction — a classical technique of analysis, not a contribution of this work — resolves this and yields a convergent width-zeta function (order O(W^-3/2) on the critical line), the DWZ method. This minimal first-order variant is used as the primary model by explicit methodological design, as the first Euler-Maclaurin order at which convergence occurs at all, not the most efficient choice. To make this auditable, we introduce a DRCC Retraction Pair formalization and an RP-Tensor selection framework, and evaluate it against our own data: on the two measured criteria, a second-order variant currently outperforms the primary model by one to two orders of magnitude, reported without adjustment. We derive a closed-form empirical estimate of the DRCC condition and add an out-of-sample check against 50 previously unused zeros, showing the aggregate trend generalizes but point-wise prediction does not. The method is reproduced against mpmath references for 100 nontrivial zeros (deviation 1.5e-6 to 1.3e-5, mean 4.87e-6, std 2.59e-6), 2 found blindly, 29 hardened via a hybrid method; a pattern hypothesis is tested (point-biserial, logistic regression, n=20) without significance. Runtime is benchmarked against Riemann-Siegel, about 30x faster and more accurate. This is a validity demonstration, not a contribution to the Riemann Hypothesis, which is not assumed.

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