Paper P3 v1. 0 of the Radial Coherential Dynamics (RCD) 2. 0 program. Constructs the axisymmetric solver for the galactic sector derived in P2 v1. 0 and closes P3-O1 by reducing the nonlocal stress-energy tensor Tₘu, nu^conf to a local quasi-static source. The reduction adopts the resummed (strong) version with full Gaussian saturation, yielding a nonlinear dependence on lambda = lK |nabla C| / C_* through the functions F₁ (lambda) and Jₜr (lambda). The effective source density rhoconf = -mu⁴ 2 F₁ (lambda) + Jₜr (lambda) is negative-definite, a nontrivial prediction of the theory. The coupled system (modified Poisson equation plus nonlinear scalar field equation) is operationally specified with computable, tabulable source functions, boundary conditions, diagnostic observable vc (r), and four kill switches. No numerical results are reported; this is the mathematical specification document. The precise Einstein-source identification remains as open problem P3-O1-bis.
Arturo Cerezo (Sun,) studied this question.