Normal-Form Resolution of a Free-Boundary MOTS Saddle-Node in Dynamical Five-Dimensional Gravity

The physical boundary of a marginally outer trapped surface (MOTS) changes the domain of its stability operator and the corresponding discrete adjoint projection. We numerically verify the local fold hypotheses for a brane-terminating MOTS pair in the SO(3)-symmetric sector of five-dimensional Einstein–anti-de Sitter gravity on a Goldberger–Wise-stabilized compact interval. An independently constructed parent sequence contains no accepted upper-brane-capped MOTS at t/ℓ = 0.001 and exactly two at t/ℓ = 0.0015 on three successive spacetime grids. Pseudo-arclength continuation locates a common critical time t*/ℓ ≃ 1.17254 × 10⁻³ in the chosen foliation. The principal stability eigenvalue crosses zero with a real, sign-definite mode; endpoint-eliminated discrete adjoint projections give nonzero transversality and quadratic coefficients; and the invariant one-sided proper-area separation follows the expected square-root law. An independent G10 half-timestep evolution gives an overlapping critical-time bracket and a free exponent p ≃ 0.498. The new result is the boundary-sensitive numerical realization, not the saddle-node mechanism itself. The claim is finite-resolution and quasi-local: it is not a continuum theorem, event-horizon reconstruction, or phase diagram.