Paper 20:Dynamical Closure of the Scale-Space Framework: Complex Scale Potential, Newtonian Recovery, and the Hidden Configurational Sector

Papers 10–11 of the Scale-Space programme established the corrected five-dimensional metric gtt = −(1 +2/L)c^2 and identified a configurational energy deficit that required a dynamical source. This paper provides that source through a systematic dynamical closure and proposes a candidate 5D covariant completion. We first identify the correct primary variable (gAB) and derive the effective scale potential ΦR = c^2/L from the Paper 10 clock factor, making L a derived parameter. The Paper 11 deficit is then rewritten as a nonlinear potential-density relation for ΦR. We show that a purely real closure leads to an unscreened logarithmic correction to Newtonian gravity that is empirically dangerous, and that this is resolved by extending ΦR to a complex scale potential Ψs = ΦR + iΦI . The action for Ψs is: LΨ = − α/2 ∇A Ψ^∗s ∇^A Ψs − αγ/4 (|Ψs|^2 − Ψ^2 0)^2 + 4πGα ρm Re(Ψs). The Euler-Lagrange equation is derived exactly and its polar decomposition yields a phase-current equation sourced by ordinary matter. Integrating over a spherical source establishes that mass sources exterior phase flux universally, and the real projection of the exterior solution recovers Newtonian gravity ΦR ≈ −GM/r at leading order, with corrections O(r^−4). The imaginary component ΦI ≈ Ψ0 − G^2 M^2 / (2Ψ0 r^2) constitutes a hidden configurational sector that carries the nonlinear scale-sector stress without appearing directly in observable gravity. All four validation tests (real-limit recovery, logarithm screening, hidden-sector regularity, observable-projection) are satisfied. We further show that superposition of phase fluxes from multiple sources recovers standard Newtonian multi-body gravity exactly. We then address the structural question of whether Ψs alone can supply the Paper 11 anisotropic background deficit. It cannot: a complex scalar yields an isotropic cosmological-constant-like stress, not the required pure clock-sector form. We resolve this by deriving a constrained configurational action with a clock-ordering covector nA, which supplies T^conf AB = E(ΦR)nA nB exactly, with E = −3 / (κ5L^3). This reproduces the Paper 11 deficit with no unwanted spatial or scale components.A candidate 5D covariant form of the full action is stated. Two items remain open: the value of Ψ0 from a background constraint calculation; and the interior solution matching.