Bulk Stabilisation and the Positivity of the Displacement Mode in the COCM

The conditional derivation of back-reaction positivity in NT8 depends on hypothesis G3: the stability of the displacement mode, m_eff^2 > 0. This note investigates a Goldberger-Wise-type route to m_eff^2 > 0 from the bulk dynamics. The central argument is that a bulk scalar field with asymmetric boundary values, sourced by the tension asymmetry tau_C0 >> tau_Rn, generates a positive curvature of the effective potential in the displacement mode. Under four explicit hypotheses S1-S4, m_eff^2 > 0 follows conditionally from the bulk dynamics. Under S1-S4 combined with G1-G4 (NT8) and H1-H3 (NT6), the full chain delta_y* > 0 -> J > 0 -> e > 0 is dynamically stabilised in two stages. The remaining open problem is S1: whether the stabilising bulk scalar arises from the COCM axioms or must be introduced as an additional ingredient.