DRCC-Width-Zeta Method (DWZ-V2.2)

Abstract

This work presents the DRCC-Width-Zeta Method (DWZ-V2.2) as a concrete operationalization of the abstract DRCC stability condition 0<d_{\mathrm{rec}}^{\mathrm{DRCC}}(X) \le d_{\mathrm{frag}}^{\mathrm{DRCC}}(X)<\infty for the Riemann zeta function. The methodological contribution is a reusable six-stage operationalization method connecting an abstract structural condition to finite numerical realization, empirical calibration, independent validation, benchmarking, and explicit documentation of limitations. Since the naive partial sum diverges in the critical strip, the numerical realization employs a classical first-order Euler–Maclaurin correction. The Euler–Maclaurin formula itself is not claimed as a new mathematical contribution; it is deliberately used as a minimal and transparent reconstruction model through which the methodology can be tested end to end. The numerical stability threshold W_{\mathrm{stab}}^{(M1)}(t,\varepsilon) is estimated empirically as an order-of-magnitude guide, not as an individually reliable predictor, a limitation quantified by the out-of-sample result R_{\mathrm{oos}}^2\approx0.08. Across 100 reference zeros, absolute position deviations range from approximately 1.5\times10^{-6} to 1.3\times10^{-5}. A complementary statistical hardening study using point-biserial correlation, logistic regression, confidence intervals, and power analysis finds no defensible relationship in the investigated n=20 sample. Benchmarking shows that the first-order DWZ method provides no algorithmic advantage and is two to three orders of magnitude slower than the tested higher-order and Riemann–Siegel approaches. This negative result is methodologically informative because it separates structural state width, numerical truncation depth, and runtime rather than treating them as interchangeable quantities. The principal contribution is therefore not a new Euler–Maclaurin formula, but a transparent, reproducible, and auditable method for operationalizing and testing an abstract DRCC condition, demonstrated through a numerical zeta instance and an exact combinatorial graph-3-coloring instance. No universal computational advantage for DRCC or contribution to proving the Riemann Hypothesis is claimed.

Keywords