Nonrepetition conjecture for the suspension-angle derivatives

For the finite layered construction $G_n(\varphi)$, let $\varphi_i(\varphi)$ denote the suspension angle at layer $i$, and let $\varphi_i'(0)$ be its derivative at $\varphi=0$. Suspension-angle derivative conjecture. The sequence $\varphi_i'(0)$ never repeats itself. If true, then sufficiently small nonzero perturbations would make the layer angles distinct and yield a geodesic net whose edges all have weight one. The conjecture is supported by numerical calculations, but remains unproved.