Orbital Ellipticity from Bulk Tension Asymmetry in the COCM: A Conditional Derivation

This note examines whether the effective orbital ellipticity e > 0 can be derived from the five-dimensional bulk geometry of C₀, without taking quasi-circularity as an external input. The COCM corpus provides an analytic expression for J in terms of bulk parameters and documents a positive proportionality between e² and J in the monograph. The central question is whether the bulk tension asymmetry τ_C₀ ≫ τ_Rn, together with the back-reaction amplitude δy > 0, suffices to force e > 0. Under two explicit hypotheses — positivity of δy and the positive proportionality encoded in the corpus relation e² ~ J — the tension asymmetry forces J > 0, and e > 0 follows without assuming quasi-circularity. The genuinely open sub-problem is the geometric origin of δy > 0: why the equilibrium position of Rn is displaced from the symmetric background.