Numerical optimization of shift profile for positive energy warp shells

We treat the shift profile of a static, spherically symmetric positive-energy warp shell as the variable of a numerical optimization problem on a fixed background (mass, radii, density and radial pressure held fixed). The objective is the critical amplitude: the first shift amplitude, on the branch connected to zero, at which any of the null, weak, strong or dominant energy conditions fails at a tested point. The search runs over a 14-parameter family (a density envelope times an exponential cubic B-spline modulation, with free exponent and switch radius), evaluated with the closed-form all-orders Eulerian stress tensor and a Hawking-Ellis eigenvalue test.