FOX Theory — Branch D: The Exterior Soliton: Asymptotic Structure, Topological Classification, and the Neutron Condition (Note to Branch C)

Branch D analyses the FOX scalar-gauge soliton in the exterior domain [r*, ∞), extending Branch C. Five results are established: K(∞) = 0 (unique fixed point); φ(∞) = φm (matter vacuum); ΔEext → 0 by oscillatory cancellation (FFT-verified); K(s*) = 1 ⟺ NCS[0,s*] = 0 (topological reformulation of the neutron condition); existence and uniqueness of K₂⁽ⁿ⁾. Three negative results close important directions. This note supplements Branch C (doi.org/10.5281/zenodo.19203591).(Version 2: N_CS[0,∞]=−1 corrected from −2; toroidal parameter p=2 replaces writhe Wr=2; charge signature phrasing clarified.)