Sharp perturbation threshold for symmetry recovery

Determine whether a sharp perturbation threshold exists for recovery of the D6 symmetry by symmetry-free neural networks approximating the dP3 Kähler–Einstein metric, and identify that threshold if it exists.

Background

The paper tests whether a symmetry-free neural network returns to a D6-symmetric solution after perturbations of different magnitudes. Recovery becomes less frequent as the perturbation size increases, but the experiment uses only twenty relaxation runs, with four seeds at each perturbation level. The observed data do not resolve whether the transition reflects a sharp threshold or a gradual change in recovery probability.