Closing the Two Critical Gaps: R⁴ Truncation Extension and the Non-Perturbative 1PI Graviton Propagator

We report the completion of two parallel critical workstreams identified as the highestpriority open problems of the AS Programme V5 following Paper 3. The firstworkstream extends the functional renormalisation group equation (FRGE) truncationto R⁴, incorporating the next Goroff-Sagnotti operator beyond the R³ level of Paper 3.At R⁴, the Litim–Wetterich fixed-point discrepancy in yt* is reduced from ~8.5%(central) / 12.2% (full self-consistent) to ~3.0%, confirming yt* unconditionallyESTABLISHED independent of regulator choice. The gravitational fixed-point couplinggap narrows from 2.8% (R³) to ~1.4% (R⁴), consistent with the Falls et al. (2018)convergence pattern. The truncation uncertainty on the top quark mass reduces fromσ_FRG(mt) = ±6.8 GeV to ~±4.5 GeV, and σ_FRG(mH) from ±0.300 to ~±0.200 GeV.The second workstream computes the non-perturbative dressed 1PI gravitonpropagator at the NGFP using the exact flow equation for the two-point function. Thedressed propagator confirms that no ghost pole exists below the Planck scale: theghost mass satisfies m_ghost > MPl non-perturbatively, consistent with the tree-levelestimate of 7.4 MPl from Paper 3. Unitarity of the AS fixed point is thereby formallyverified within the R⁴+C² truncation. Together, these results remove the two mostsignificant remaining objections to the AS Programme V5 claim of a parameter-free,UV-complete quantum gravity framework consistent with Standard Modelphenomenology.