Two-Boundary Determination of the Cosmological Constant from Asymptotic Safety and Gravitational Feedback

The cosmological constant problem — why the observed vacuum energy is roughly 10¹²⁰ times smaller than the Planck scale — has resisted solution for decades and driven much of theoretical physics toward anthropic reasoning. We argue that Λ is not the outcome of an improbable cancellation, nor a selection effect in a multiverse, but the unique solution of a boundary-value problem on the gravitational renormalisation group (RG) flow. One boundary condition comes from the ultraviolet: the Reuter fixed point of asymptotic safety, which restricts quantum gravity to a low-dimensional critical surface. The other comes from the infrared: the structure-formation feedback attractor established in Paper I (Salmond 2026, The Cosmological Constant as a Feedback Attractor; hereafter Paper I), which fixes Λ through gravitational self-consistency with bounded sensitivity. The key observation is that the dimensionless cosmological constant λ (k) = Λ/k² is O (1) at both boundaries — λ* ≈ 0. 19 at the Planck scale and λ (H₀) ≈ 2. 07 at the Hubble scale — so the 10¹²⁰ between them is simply the squared ratio of these scales, not a tuning. Two conditions on a two-dimensional surface generically fix a unique RG trajectory, hence a unique Λ, with combined robustness Eₜotal < 10⁻⁷⁰: perturbations to Planck-scale physics are exponentially irrelevant for the late-universe vacuum energy. Using published fixed-point data from eleven truncations of the exact renormalisation group equation, we show that the predicted Λ turning point lies within a factor 3–4 of the Hubble scale in every case, providing a candidate resolution of the coincidence problem that does not require anthropic reasoning. We demonstrate analytically that Standard Model threshold corrections preserve the Jacobian of the critical-surface map exactly, and identify the precise condition for the programme's success: that continuous, trajectory-dependent matter-loop running — where vacuum-energy contributions decouple as m⁴/k⁴ while Newton-constant contributions decouple as m²/k² — breaks the rank-1 degeneracy of the pure-gravity flow. Conditional on this rank condition, the 10¹²⁰ cosmological constant problem reduces to a concrete, computable rank-condition problem on the gravitational flow equations with Standard Model matter, rather than being resolved outright. The decisive numerical check (Computation B, §11) has not yet been performed.