Does the COCM Axiomatic Structure Generate a Stabilising Bulk Scalar? A Scan of P4 for Hypothesis S1

The conditional derivation of displacement mode stability in NT9 depends on hypothesis S1: the existence of a bulk scalar field consistent with the COCM framework that generates positive curvature of the effective orbital potential. S1 was introduced by analogy with the Goldberger-Wise mechanism but was not derived from the corpus axioms. This note addresses PG directly: does the axiomatic structure of P4 already contain a candidate stabilising scalar, or must one be introduced as a new ingredient? We scan the six axioms of P4 for elements that could generate a scalar sector in the bulk. The result is conditional: the p-brane DBI action of Axiom A4 contains a scalar degree of freedom -- the transverse position field delta_y -- whose effective potential under the tension asymmetry acquires a positive curvature consistent with NT9. This does not constitute a full derivation of S1, but it identifies a natural candidate within P4 that reduces PG to a single calculational question: whether the back-reaction profile f(y) is concave at the brane position.