We study effective randomness-preserving transformations of path-incompressible trees. Some path-incompressible trees with infinitely many paths do not compute perfect path-random trees with computable oracle-use. Sparse perfect path-incompressible trees can be effectively densified, almost surely. We characterize the branching density of path-random trees.

翻译：我们研究路径不可压缩树的有效随机性保持变换。某些拥有无穷多条路径的路径不可压缩树，无法通过可计算的神谕使用来计算出完美的路径随机树。稀疏的完美路径不可压缩树几乎必然可以被有效稠密化。我们对路径随机树的分支密度进行了刻画。