Resolving the Spin-2 Boundary Layer in f(R) Asymptotic Safety

The functional renormalization group equation for f(R) quantum gravity possesses a well-studied non-Gaussian fixed point (NGFP) in the ultraviolet, but attempts to flow the full, nonlinear f̃(R̃) equation from this fixed point to the deep infrared (R̃ → 0) have historically encountered a singular barrier: the denominator of the spin-2 trace mode crosses zero, causing numerical simulations to diverge. This has been widely regarded as a structural obstruction to extracting IR predictions from the f(R) flow. We resolve this obstruction. We demonstrate that the barrier is not a physical singularity but an ultra-thin boundary layer of width δ ∼ 1.6 × 10⁻⁷ in dimensionless curvature — two orders of magnitude thinner than the finest achievable finite-difference grid spacing, explaining the failure of all prior numerical approaches. By reformulating the fixed-point equation as a spatial ODE and shooting inward from the UV polynomial regime with a stiffly-stable implicit solver (Radau IIA), we navigate the pole crossing as a removable singularity — the unique trajectory where numerator and denominator vanish simultaneously. Inside the boundary layer, the spin-2 trace resonance suppresses the R² coupling g₂ by five orders of magnitude while leaving the cosmological (g₀) and Newtonian (g₁) couplings essentially unchanged — a scale separation that makes the dimensionless cosmological constant Λ̃ = −g₀/(2g₁) structurally stable, varying by less than 10⁻⁴ across three orders of magnitude in Aₛ. At the n = 6 polynomial truncation level with Standard Model matter, the separatrix yields Λ̃ = −0.7318 — a negative (anti-de Sitter) value. This negative sign is a stable property of the SM f(R) NGFP from n = 3 through n = 6 (Paper IV), but differs from the positive λ* = 0.15 found in the Einstein–Hilbert truncation with the same matter content (Donà, Eichhorn & Percacci 2014). We establish a three-way closure on the sign question within the polynomial f(R) truncation: (i) extending to n = 8 confirms Λ̃ converging at ≈ −1.11, drifting further negative; (ii) a comprehensive landscape scan of all SM fixed points at n = 3 finds no positive-Λ̃ branch at any dim(S_UV); (iii) a Phase 2 RG time flow rules out late-time electroweak threshold corrections (10⁶⁸× too small to flip the sign). The resolution must lie in the non-polynomial regime, beyond f(R), or in a modified matter prescription at the NGFP scale.