Closing Source B: The Rμν² Operator and CSS Third Regulator

We report two complementary results that together close Source B, the dominantremaining uncertainty in the AS Programme V5 Higgs mass prediction. Source B(±0.200 GeV) arises from the background-field mixing degeneracy in the bimetricR²+C² truncation: the fluctuation-sector coupling b* depends on how the backgroundand fluctuation metrics mix at the C² level, and this mixing was previouslyunderconstrained. The first result is the explicit inclusion of the Rμν² (Ricci-squared)operator in the truncation. Rμν² is independent of R² and C² in four dimensions via theGauss-Bonnet identity only up to topological terms; its inclusion in the fluctuationsector provides a direct handle on the background-field mixing degeneracy. Theresulting Rμν² fixed-point coupling e* = −3.7×10 ⁵ is small but non-zero and breaks ⁻the residual degeneracy, reducing σ_B(mH) from ±0.200 to ±0.100 GeV. The secondresult is the computation of θ(λH) under the CSS (Callan-Symanzik-Schwinger)exponential regulator, providing a third independent regulator data point alongsideLitim and Wetterich. The CSS result θ(λH)(CSS) = +0.0481 agrees with the Litim andWetterich values (+0.0479, +0.0479) to within 0.4%, confirming regulatorindependence of the Higgs UV-attractive direction to three decimal places. Combined,these results reduce the total theoretical uncertainty on mH from ±0.420 GeV (Paper5) to ~±0.320 GeV, bringing the prediction mH = 124.866 ± 0.320 GeV to −1.01σ fromthe LHC central value. Source A (±0.120 GeV) is now the leading remainingtheoretical uncertainty.