Covariance scaling and a dual-mode torque diagnostic in measurements of the gravitational constant

Abstract

Laboratory determinations of the Newtonian gravitational constant $G$ disagree by more than their quoted uncertainties allow. We examine the sixteen determinations comprising the CODATA-2018 archive using a proportional covariance-scale model that retains the full reported covariance matrix. Because the 2026 NIST torsion-balance redetermination shares apparatus lineage with the BIPM Mark II balance, our primary historical fit excludes the BIPM-14 determination, giving $\hatλ = 2.967$ for the remaining fifteen measurements. Evaluated against this historical model under the declared uniform covariance-scaling convention, the correlated four-configuration NIST result is highly unlikely under the archive's reported, unscaled covariance but is statistically unremarkable once the historically inferred extra dispersion is applied ($Q_λ= 4.840$; finite-sample $F$ tail $p = 0.382$); a mean-only scaling sensitivity leaves the vector discrepant. Retaining the complete archive also gives a comparable result. We further examine four matched free-minus-servo torque differences reported by NIST. They are consistent with a single common absolute torque offset across the four tested configurations, $\widehat{ΔN} = 1.918 \pm 0.215$ pN m, and poorly described by an equally simple fractional-scale alternative under the stated independent-Type-A treatment, with a chi-square contrast of $Δχ^{2} = 11.041$ between the two torque models. The paper provides a covariance audit of the historical archive, a lineage-qualified consistency check, and an experimentally testable diagnostic for dual-mode torsion balances, without proposing a revised value of $G$.