Counterexamples to Conjectures 3 and 4 of Huang, Stoica, Xia and Zhong (arXiv:2006.06716v1, Section 5.2, printed page 32)

Conjectures 3 and 4 in Section 5.2 of Huang, Stoica, Xia and Zhong, arXiv:2006.06716v1, printed page 32, are refuted by positive nonconstant solutions of their tree equations of motion. For every integer q >= 2, r > 0 with r != 1 and t > 0, spine lengths ((r^2+1)/(r+1)) t r^n and constant-length branches t r^n give a solution. Every branch vertex has equal incident lengths. More generally, a positive solution on any connected nontrivial tree of maximum degree at most q+1 extends to T_q by attaching constant-length branches without changing its original vertex ratios. The source's line classification yields arbitrary two-choice spine patterns in all q >= 2. The geometric-spine solutions have nonconstant tree curvature.