From a Free-Boundary MOTS Saddle-Node to a Spacelike Marginal Tube in Dynamical Five-Dimensional Gravity

Pair creation is a local statement about marginally outer trapped surfaces (MOTSs); its physical significance depends on what the stable branch becomes. We resolve both the critical creation and the subsequent geometric development of brane-terminating MOTSs in the SO(3)-symmetric sector of a dynamically evolved, Goldberger–Wise-stabilized five-dimensional spacetime. An independently constructed parent sequence contains no accepted 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 through a real sign-definite mode; discrete adjoint projections give nonzero transversality and quadratic coefficients; and the invariant one-sided proper-area separation follows the predicted square-root law. An independent G10 half-timestep evolution reproduces the critical bracket and gives a free exponent p ≃ 0.498. We then follow the stable outer branch over nine evenly spaced matched leaves spanning 0.00121875 ≤ t/ℓ ≤ 0.00146875, with physical leaf spacing 3.125 × 10⁻⁵ ℓ. It forms a resolved spacelike marginal tube with negative inward expansion, strictly increasing area, positive principal stability, and orthogonal brane contact. Its geometry and causal signature transfer across G9/G10/G11 and survive the half-timestep evolution. A brane-inclusive reflected quasi-local charge ledger closes over a finite segment with a worst charge–flux discrepancy of 0.302%, robust under three spatial stencils. The combined result traces a boundary-created stable branch from its saddle-node through a finite-resolution free-boundary dynamical-horizon segment. It remains quasi-local and foliation-dependent and is neither a continuum theorem nor an event-horizon, global-topology, or source-ownership reconstruction.