We present FOX Theory (Flow of eXtremes, Branch A), a pre-geometric scalar field framework in which a dimensionless field φ = Φ/ΦMAX ∈ 0, 1 couples to gravity through the Palatini action. The linear coupling f (R̃) = R̃ is the unique choice consistent with the causal priority of the connection (Postulate P4). Four results are established. (i) In the Palatini formulation, the gravitational energy-momentum tensor contains no second-derivative terms, so the post-Newtonian parameter γ = 1 exactly. (ii) The equilibrium condition V' (φₘ) = 0 at the matter minimum implies Gₑff = G to linear order in perturbations. (iii) The Palatini torsion integral over the radial profile of a spin-1/2 fermion equals 4π exactly, yielding φᵢn = exp (−4π) ≈ 3. 5×10⁻⁶. We further derive the analytical curvature profile R (φ) = C√|Z (φ) | with Z = 2φV' − 2V, establish a Derrick-type no-go showing that the scalar potential alone cannot stabilize any FOX field configuration, and identify three open limits requiring extension of the present framework.
Adrien le Hardy de Beaulieu (Sat,) studied this question.