THE ABÏON METRIC Parametric Topology Optimization

We present the complete parametric optimization of the double-surface topology underlying the ABÏON warp-drive geometry — a hybrid configuration consisting of an outer hyperboloidal shell rotating at angular velocity +ω and an inner paraboloidal shell counter-rotating at −ω. The optimization seeks to maximize the Anti-Venturi effect: the geometric property whereby the inter-shell separation at the throat exceeds the separation at the mouths, thereby concentrating momentum density T⁰ⁱ in the region of maximum frame-dragging coupling. A two-stage optimization strategy is employed: stochastic exhaustive search over 156,800 discretized combinations followed by differential evolution over the continuous six-dimensional parameter space. The resulting global optimum achieves a throat separation of 86.3 m, a mouth separation of 43.2 m, and an exact d_max/d_min ratio of 2.00. Sensitivity analysis reveals that the score surface is dominated by two parameters (exterior throat radius and device semi-length), while the remaining four exhibit robust tolerance under ±20% perturbation. Keywords: ABÏON metric, warp drive, topology optimization, Anti-Venturi effect, frame-dragging, differential evolution, hyperboloid-paraboloid geometry, parametric design, momentum density concentration, General Relativity