  This is the first in a series of papers by the authors on the arborealization
program. The main goal of the paper is the proof of uniqueness of arboreal
models, defined as the closure of the class of smooth germs of Lagrangian
submanifolds under the operation of taking iterated transverse Liouville cones.
The parametric version of the stability result implies that the space of germs
of symplectomorphisms that preserve a canonical model is weakly homotopy
equivalent to the space of automorphisms of the corresponding signed rooted
tree. Hence the local symplectic topology around a canonical model reduces to
combinatorics, even parametrically.
