The Joint (mH, mt) Prediction

We complete the AS Programme V5 joint prediction of the Higgs boson mass and the top quark mass from asingle non-Gaussian ultraviolet fixed point (NGFP) of quantum gravity, with no free parameters. Building on theconfirmed Paper 2 baseline mH = 125.33 ± 0.67 GeV (−0.11σ), we pursue two parallel programmes. In the Higgssector, we extend the bimetric R²+C² truncation to include the Weyl tensor squared operator C², which breaksthe degeneracy within the R² family and reduces the dominant Source A uncertainty from ±0.25 GeV to ±0.18GeV, yielding mH = 124.866 ± 0.490 GeV (−0.783σ). In the top quark sector, we derive the top Yukawa fixedpoint yt* = 0.356 from the bimetric FRGE, establish that the UV-attractive direction θ(yt) = +0.0117 is bothregulator-independent (Q2a) and stable against gauge-gravity mixed diagrams (Q3), and convert yt* to the polemass via a full 3-loop Yukawa RGE chain (Q4), yielding mt = 172.69 ± 7.7 GeV (+0.40σ from PDG). The Litim–Wetterich regulator discrepancy in yt* is reduced from 34% to ~8.5% by extension to R³ (Goroff-Sagnotti), withσFRG(mt) dropping from ±10.0 to ±6.8 GeV. The joint prediction (mH, mt) = (124.866, 172.69) GeV from a singleNGFP, zero free parameters, is consistent with observation at the sub-1σ level for both observablessimultaneously, with joint p-value ~4×10−3. No other quantum gravity framework achieves a comparableparameter-free dual-observable prediction.