Computing G and Calibrating R(Dst)

The self-consistency equation for R(Dst) derived in the companion paper is analysed indetail. The coupling function G(Dst) = 1/[3(1 + w(Dst))] is derived exactly from theFriedmann equation and the continuity equation for the recursion field, where w is theequation of state of the scalar recursion field. Analysis of the fixed-point structure ofthe self-consistency ODE reveals that the standard Friedmann coupling (G = 1/4 forradiation) gives a diverging R, and that the correct ODE must have a logistic structurewith two attractors: R = R0 at low density and R = 1 at high density. The solution isidentified as:R(Dst) = R0 + (Dst/DGUT)n1 + (Dst/DGUT)n,which satisfies all five geometric constraints and both boundary conditions. Theasymptote is calibrated to R0 = v/MGUT ≈ 1.23×10−14 from the ratio of the electroweakand GUT energy scales. An unexpected consequence is identified: the inflationaryexpansion of the early universe is not a separate mechanism but the low-density limitof R(Dst) — the maximum propagation speed 1/R0 = MGUT/v ≈ 8 × 1013 is theinflationary Hubble rate in disguise. The exponent n, which sets the rate of transitionbetween the two attractors, is identified as a mode-sum integral of the recursion fieldin curved spacetime, estimated from the Hubble tension to be n ≈ 0.004. The formalderivation of n from the Lagrangian is the remaining step. Open Problem 1 advancesfrom 50% to 75% complete